This list is my first bigger "research" post on this page so have mercy on me in case of mistakes, a discussion is welcome anyway.
The question which state is "visually" dominated by which carrier has been occupying myself for a while so I finally decided to take a closer look at it.
I did not find any similar threads searching the forum but I know the search engine doesn't always fulfil its purpose quite well, so should this already exist in some way, consider my post an updated version or delete it if necessary. I won't take it personal

So now the criteria I chose: I would decide "strongest presence" by the NUMBER OF AIRPORTS an airline currently flies into in a state (lower 48) - the carrier which has most, wins the state in a "winner takes it all"-way, like the US presidential elections. I will for every state name the winning carrier as well as listing the destinations.
I do count regional subsidiaries into an airline (Eagle = AA; Delta Connection = DL; UAX = UA; US Express = US) but I will not count EAS carriers as long as they don't operate under the brand of a major carrier, otherwise the results would be somewhat falsified as I count only the number of airports and not passenger numbers. At the end of the table I will upload a map with every state colored according to its predominant carrier.
As I wrote above, if there are any criticisms or i.e. airports I forgot to count, feel free to correct me.
Enjoy!
ALABAMA > * DL Delta Air Lines/Delta Connection*
MGM Montgomery
MOB Mobile
HSV Huntsville
DHN Dothan
BHM Birmingham-Shuttlesworth
-
ARIZONA > * US US Airways/US Airways Express *
YUM Yuma
TUS Tucson
PHX Phoenix Sky Harbor
FLG Flagstaff
-
ARKANSAS > * AA American Airlines/American Eagle *
TXK Texarkana
LIT Little Rock
FSM Fort Smith
XNA Fayetteville / Northwest AR
-
CALIFORNIA > * UA United Airlines/United Airlines Express *
SMX Santa Maria
SBA Santa Barbara
SNA Santa Ana / Orange Co.
SBP San Luis Obispo
SJC San José
SFO San Francisco
SAN San Diego
SMF Sacramento
RDD Redding
PSP Palm Springs
ONT Ontario
MRY Monterrey
MMH Mammoth / Yosemite
LAX Los Angeles
FAT Fresno
CEC Crescent City
CLD Palomar
BUR Burbank
BFL Bakersfield
ACV Arcata-Eureka
-
COLORADO > * UA United Airlines/United Airlines Express *
PUB Pueblo
MTJ Montrose
HDN Hayden
GUC Crested Butte
GJT Grand Junction
EGE Eagle County / Vail
DRO Durango
DEN Denver
COS Colorado Springs
ASE Aspen
-
CONNECTICUT > * US US Airways/US Airways Express *
HVN New Haven
BDL Windsor Locks
-
DELAWARE > * F9 Frontier Airlines *
ILG Wilmington DE
-
FLORIDA > * DL Delta Air Lines/Delta Connection * [very closely followed by US with just 1 destination short]
PBI Palm Beach
VPS Valparaiso
TPA Tampa
TLH Tallahassee
SRQ Sarasota
PNS Pensacola
ECP Northwest Florida
MCO Orlando McCoy
MIA Miami
MLB Melbourne
EYW Key West
JAX Jacksonville
GNV Gainesville
RSW Fort Myers
FLL Fort Lauderdale
DAB Daytona Beach
-
GEORGIA > * DL Delta Air Lines/Delta Connection *
VLD Valdosta
SAV Savannah
CSG Columbus GA
BQK Brunswick
AGS Augusta
ATL Atlanta
ABY Southwest Georgia
-
IDAHO > * DL Delta Air Lines/Delta Connection *
TWF Twin Falls
PIH Pocatello
LWS Lewiston
IDA Idaho Falls
SUN Friedman
BOI Boise
-
ILLINOIS > * TIED in numbers between G4 Allegiant Air and AA American Airlines/American Eagle *
G4 Destinations:
BLV Saint Louis / MidAmerica
BMI Bloomington
MLI Moline
PIA Peoria
RFD Rockford / Chicago
SPI Springfield IL
AA Destinations
BMI Bloomington
CMI University of IL
ORD Chicago-O'hare
MLI Moline
PIA Peoria
SPI Springfield IL
-
INDIANA > * TIED in numbers between DL Delta Air Lines/Delta Connection and UA United Airlines/United Airlines Express *
BOTH serving:
SBN South Bend
IND Indianapolis
FWA Fort Wayne
EVV Evansville
-
IOWA > * AA American Airlines/American Eagle *
CID Cedar Rapids
DSM Des Moines
DBQ Dubuque
SUX Sioux City
ALO Waterloo
-
KANSAS > * AA American Airlines/American Eagle *
ICT Wichita
MHK Manhattan KS
GCK Garden City
-
KENTUCKY > * UA United Airlines/United Airlines Express *
PAH Paducah
SDF Louisville
LEX Lexington
CVG Cincinnatti
-
LOUISIANA > * TIED in numbers between AA American Airlines/American Eagle and UA United Airlines/United Airlines Express *
BOTH serving:
SHV Shreveport
MSY New Orleans
MLU Monroe
LCH Lake Charles
LFT Lafayette
BTR Baton Rouge
AEX Alexandria
-
MAINE > * TIED in numbers between UA United Airlines/United Airlines Express and DL Delta Air Lines/Delta Connection and US US Airways/US Airways Express *
ALL serving:
PWM Portland ME
BGM Bangor
-
MARYLAND > * US US Airways/US Airways Express *
SBY Salisbury
BWI Baltimore
-
MASSACHUSETTS > * B6 jetBlue Airways *
ORH Worcester
MVY Martha's Vineyard
ACK Nantucket
HYA Barnstable
BOS Boston
-
MICHIGAN > * DL Delta Air Lines/Delta Connection *
TVC Traverse City
CIU Chippewa Co
MBS Saginaw
PLN Pellston
MQT Marquette
LAN Lansing
AZO Kalamazoo / Battle Creek
GRR Grand Rapids
FNT Flint
ESC Escanaba
DTW Detroit
APN Alpena
-
MINNESOTA > * DL Delta Air Lines/Delta Connection *
RST Rochester MN
MSP Minneapolis
INL International Falls
HIB Hibbing
DLH Duluth
BRD Brainerd
BJI Bemidji
-
MISSISSIPPI > * AA American Airlines/American Eagle *
MEI Meridian
JAN Jackson
PIB Hattiesburg
GPT Gulfport / Biloxi
-
MISSOURI > * AA American Airlines/American Eagle *
STL Saint Louis
SGF Springfield MO
MCI Kansas City
JLN Joplin
COU Columbia MO
-
MONTANA > * DL Delta Air Lines/Delta Connection *
MSO Missoula
FCA Glacier Park
HLN Helena
GTF Great Falls
BTM Butte
BZN Bozeman
BIL Billings
WYS West Yellowstone
-
NEBRASKA > * TIED in numbers between DL Delta Air Lines/Delta Connection and AA American Airlines/American Eagle and UA United Airlines/United Airlines Express *
AA destinations:
GRI Grand Island
OMA Omaha
DL and UA both serving:
LNK Lincoln
OMA Omaha
-
NEVADA > * DL Delta Air Lines/Delta Connection *
RNO Reno
LAS Las Vegas
EKO Elko
-
NEW HAMPSHIRE > * every airline flying into NH only has one destination in the state *
PSM Portsmouth
MHT Manchester / Boston
-
NEW JERSEY > * AC Air Canada/Air Canada Express *
EWR Newark
ACY Atlantic City [starting May]
-
NEW MEXICO > * TIED in numbers between AA American Airlines/American Eagle and UA United Airlines/United Airlines Express *
UA destinations:
HOB Hobbs
SAF Santa Fe
ABQ Albuquerque
AA destinations:
ROW Roswell
SAF Santa Fe
ABQ Albuquerque
-
NEW YORK > * US US Airways/US Airways Express *
HPN White Plains
ART Watertown
SYR Syracuse
ROC Rochester
SWF Newburgh
LGA New York-LaGuardia
JFK New York-John F Kennedy
ITH Ithaca
ISP Islip
ELM Elmira
BUF Buffalo
BGM Binghampton
ALB Albany
-
NORTH CAROLINA > * US US Airways/US Airways Express *
ILM Wilmington NC
RDU Raleigh-Durham
EWN New Bern
OAJ Jacksonville NC
PGV Greenville NC
GSO Greensboro
FAY Fayetteville
CLT Charlotte
AVL Asheville
-
NORTH DAKOTA > * TIED in numbers between DL Delta Air Lines/Delta Connection and UA United Airlines/United Airlines Express *
BOTH serving:
ISN Williston
MOT Minot
FAR Fargo
DIK Dickinson
BIS Bismarck
UA destination:
DVL Devil's Lake
DL destination:
GFK Grand Forks
-
OHIO > * TIED in numbers between DL Delta Air Lines/Delta Connection and UA United Airlines/United Airlines Express and WN Southwest Airlines and US US Airways/US Airways Express and AA American Airlines/American Eagle *
ALL serving:
DAY Dayton
CMH Port Columbus
CLE Cleveland
WN, UA, US, DL serving:
CAK Akron-Canton
AA destination:
TOL Toledo
-
OKLAHOMA > * AA American Airlines/American Eagle *
TUL Tulsa
OKC Oklahoma City
LAW Lawton
-
OREGON > * UA United Airlines/United Airlines Express *
RDM Redmond
PDX Portland OR
OTH North Bend
MFR Medford
EUG Eugene
-
PENNSYLVANIA > * US US Airways/US Airways Express *
IPT Williamsport
AVP Wilkes-Barre
SCE State College
PIT Pittsburgh
PHL Philadelphia
MDT Harrisburg
ERI Erie
ABE Allentown
-
RHODE ISLAND > * every airline flying into RI only has one destination in the state *
PVD Providence
-
SOUTH CAROLINA > * US US Airways/US Airways Express *
MYR Myrtle Beach
HHH Hilton Head Island
GSP Greenville SC-Spartanburg
FLO Florence
CAE Columbia SC
CHS Charleston
-
SOUTH DAKOTA > * DL Delta Air Lines/Delta Connection *
FSD Sioux Falls
RAP Rapid City
ABR Aberdeen
-
TENNESSEE > * TIED in numbers between DL Delta Air Lines/Delta Connection and US US Airways/US Airways Express and AA American Airlines/American Eagle *
ALL serving:
BNA Nashville
MEM Memphis
TYS Knoxville
CHA Chattanooga
-
TEXAS > * AA American Airlines/American Eagle *
SPS Wichita Falls
ACT Waco
TYR Tyler
SAT San Antonio
MAF Midland
MFE McAllen
LBB Lubbock
GGG Gregg Co
LRD Laredo
HOU Houston-Hobby
IAH Houston-Intercontinental
GRK Killeen-Ft Hood
ELP El Paso
DFW Dallas-Ft Worth
CRP Corpus Christi
CLL College Station
BRO Brownsville
BPT Port Arthur
AUS Austin
AMA Amarillo
ABI Abilene
-
UTAH > * DL Delta Air Lines/Delta Connection *
SGU St George
SLC Salt Lake City
VEL Vernal
CNY Moab
CDC Cedar City
-
VERMONT > * every airline flying into VT only has one destination in the state *
BTV Burlington
-
VIRGINIA > * US US Airways/US Airways Express *
IAD Washington-Dulles
DCA Washington-Reagan
ROA Roanoke
RIC Richmond
ORF Norfolk
PHF Newport News / Williamsburg
LYH Lynchburg
CHO Charlottesville
-
WASHINGTON > * AS Alaska Airlines/Horizon Air *
YKM Yakima
EAT Wenatchee
ALW Walla Walla
GEG Spokane
SEA Seattle-Tacoma
PUW Pullman / Moscow
PSC Pasco
BLI Bellingham
-
WEST VIRGINIA > * UA United Airlines/United Airlines Express *
LWB Lewisburg
CHW Charleston WV
PKB Parkersburg
-
WISCONSIN > * DL Delta Air Lines/Delta Connection *
RHI Rhinelander
CWA Mosinee
MKE Milwaukee
MSN Madison
LSE La Crosse
GRB Green Bay
ATW Appleton
-
WYOMING > * UA United Airlines/United Airlines Express *
RKS Rock Springs
LAR Laramie
JAC Jackson Hole
GCC Gillette
COD Cody / Yellowstone
CPR Casper
Congratulations to all who have made it through this behemoth of a list - took me beyond 3 hours to create

Here is the map:
