Stacks are 2000 and blinds are 10/20 vs unknown.

Villain raises to 60 I 3 bet with A8s to 180 he calls. Flop comes 6h7h8c I check villain bets a bit more then 1/2 pot, hero ?..

I decided to check shove which maybe is too extreme? Because a lot of the hands he calls with we're flipping or I'm close to drawing dead. Is it more +ev to just call here and take one card off? I tend to do stuff like this a lot on draw heavy boards.