Yes the J-15 is heavy, but it makes up for it with one of the longest range and biggest payload of any carrier fighter and heavy carrier fighters were once the norm (hint F-14), yes it is a 30 year old design, and so is the F-18 and the Etendard and yet they are still flying fine.
We don't have weight or range figures for j-15 but su-33 isn't that good in those departments.
Ferry range figures, using external tanks then dropping them when empty. Taking off from land:
Su-33 3000 km
Mig29k 3000 km
F35c around 3000 km (estimate only since no figure is disclosed)
Harrier ii+ 3300 km
F18c 3400 km
F18e 3400 km
Rafale m 3700 km
F14d could do some 3100 km. (A model was better)
Super etendard could do 3300 km (despite what wiki says) but it has been retired and no longer serves.
Of course, ferry ranges can't simply be halved to get operational ranges. Different missions would change combat ranges differntly. Small planes would do a bit worse with heavy loads. Taking off from a carrier would especially make it hard to to comparisons.
Empty Weight to thrust ratio is also not really top of the line for su-33.
Su33 19 tons for 255 kn 13.4
F18c ~11 tons for 158 kn 14.4
F18e 14.5 t for 196 kn 13.5
Rafale m 10.5 t for 150 kn 14.3
Mig29k 11-12 tons for 176 kn 15.3
F35c 15.7 tons for 191 kn 12.16
Of course operative thrust to weight ratio is a bit different, especially when heavier loads are used.
As said, though, su33 operating from forward launch positions won't get as close to its potential, compared to most other planes here.