With european LCCs you will get zero (piece or bags) for free or sometimes 15 kg.
If considering flying FR
you will get to GRO
but not to BCN
(form London). Plus you will have to transfer from presumably LHR
- unless you find flights to connect at LGW
In sum, a major hassle.
A single bag of 15 kg max will be extra 15 €, one bag of max. 20 kg -> 25 €. Excess weight is handled very strictly and it costly.
Question: Will you be able to limit your checked baggage to only 15 kg ( = 33 lbs) for a one-week cruise ?
Consider to look into flying AB
and then on to BCN
Or are there any cruises starting on the island of Mallorca (Majorca) ? Then fly DUS
OTOH, July/August is high season for Mallorca, whereas Barcelona will be deserted by locals in August due to weather & vacation. So, flights into BCN
could be the better option.
Flying into MAD
and then take an AVE-train to Barcelona indeed is an option. If it is viable financially you will have to decide.
Keep in mind that, if you book your flight NYC - BCN
on one PNR, the "picece concept" will be applied for feeder flights in Europe (and not a "weight concept"). This actually might work favorably for you.
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !