I think you played this fine, can you show the flop play? UTGs stack size gives you awesome set odds to play your hand if he does have a strong hand, also if you 3 bet decently here theres a chance the big stack will shove over with hands like AA/KK/QQ/AK.

If it was headsup with the shortstack id probably 4bet shove here oop.

Note. Im a noob there will be much better advice to come