How is weight relevant here? You design your ship around your requirements, not the other way around. The point been J-20 is smaller than J-15.
You are assuming J-20 is very small. It is not so.
You will also end up with a STOBAR configuration rather than CATOBAR.
Weight matters because the engines should be able to throw all that weight out quickly while guzzling less fuel.
No matter how small the J-20 is, it won't be smaller than a SH. I am pretty sure PLAN will be looking forward to operate CATOBAR systems rather than STOBAR.
If Liaoning can have J-15s, then there should be no problem for navalized J-20 on future ACs.
That doesn't mean much. The Mig-29K is a far superior platform compared to the J-15 since both are STOBAR systems. Mig-29K can take off at MTOW from a small ship like Gorky while even a Kuznetsov class ship cannot help the J-15 in taking off at MTOW. Space constraints will be too much.
You are much better off if you have a smaller Mig-29K class aircraft with CATOBAR capability, like Rafale.
You will have more numbers and more capability with a CATOBAR system.
Go figure why the Russians have decided to go for Mig-29Ks on the Kuznetsov rather than simply upgrading the J-15 like the VVS is doing with old Su-27s. Double the numbers and increased capability.