question on AK

say you raise with AK in late position and a limper from MP or MP+1 calls you. the flop is all below 10 and he checks and you bet and he calls, the turn is another blank and another check, a bet and a call. the river hits another blank and he checks, should I bet again even though he's called me down the whole way or do i check? Over the long run, whats the correct play here? Sorry for no hand history, just a strategy question. Oh yeah, no flush or straight possibilities