It tough to say without any reads. I don't know exactly what you mean by “don't believe his 3bet”, its not often he is on total air so he has a range of decent hands he's making this with. Given the dynamics your hand is ahead of that range so I don't mind 4betting.

Now i'm trying to range this player here and think its pretty strong. I entered into pokerstove some ranges :

1) TT+,88,AJs+,KQs,AQo+

     -Against this range we have roughly 52% equity. Granted KQs may be a little loose as well as 88 for some players. This range gets even wider when we toss in AJo, A10s, a few random Axs even maybe 77 so add those in we pick up even more equity.

So given that we are never crushing postflop or getting crushed so I think we have to make a decision on whether we want to be getting our stack in. We gotta factor in alot of things, our edge against the field, where we stand to be if we win/lose etc etc.

So on the flop, I'm not too uncomfortable getting it all in. But I think when you lead there and call off you aren't allowing the player to bluff or make a move on the pot with the part of his range that really hasn't connected. I think if you check that flop you are allowing certain hands in his range that don't connect well or are scared or that connected board. When you lead it really eliminates alot of his range and he's only gonna proceed with hands you aren't too happy about getting it in again.