Basically: yes, the ER designation is based on MTOW for both the 747 and 777 derivatives.
The 747-400 is available at weights up to 396,900kg (875,000lb). The -400ER starts at 412,775kg (910,000lb). This MTOW difference is due to the heavier structure, undercarriage and wings of the -400ER -- which retains some components designed for the -400F. Other, less significant, upgrades are also featured on the -400ER (front wingroot fairing, cockpit upgrades, etc.).
As far as the 777-200 is concerned:
o The "A-market" derivatives (-200)
are airplanes at weights between 229,520kg (506,000lb) and 247,210kg (545,000lb).
o The "B-market derivatives (-200ER, formerly -200IGW)
are airplanes at weights between 263,080kg (580,000lb) and 297,560kg (656,000lb).
Hope that helps. If you are interested in more details on the 747-400 vs. -400ER differences: Boeing 747-400X, ER & QLR
Air Transport Business