100 BB deep, unknown guy sits me.

Villain raises from btn 3x I 3bet with AKo slightly bigger then 3x his raise and he calls. Flop comes 3cThJs I cbet 1/2 pot he calls turn comes 6h I bet 60% of pot he calls river comes Kh and I shove.

Is it better to check call or even check fold to a shove here then to shove myself? I feel lost in spots like these.