flopped set with deep stacks

[M.B.E.]

From a $109 "deep-stack" tournament on PokerStars.

Blinds 15/30, UTG+2 (9K stack) raises to 90. I call in MP with 3[img]/images/graemlins/spade.gif[/img]3[img]/images/graemlins/diamond.gif[/img] (8K stack). BB (3K stack) reraises to 240. Original raiser calls, I call.

Flop 5[img]/images/graemlins/heart.gif[/img]4[img]/images/graemlins/heart.gif[/img]3[img]/images/graemlins/heart.gif[/img]

BB pushes, 2772 into a 735 pot. Since I've been at the table, he's pushed like this a couple of times, one time preflop he openpushed for 120x the BB with AK, another time he pushed the flop but the hand didn't get shown.

The other guy thinks a bit and calls. I considered calling, folding, and raising, and elected to call.

Now the three-way main pot has 9051 chips and I have 4771 behind, heads-up on the side. My opponent has me covered by 1300 chips. Turn is the 8[img]/images/graemlins/heart.gif[/img] and my opponent checks. Should I check behind, or push? And did I make a mistake on the flop?