I totally agree with either bet folding the turn or bet calling and call river if you think your 8 pair is good. Let try to analyse your play: Inititally, you min raise preflop, most of the time only AA or KK will do that so that opp will call light or induce a 3bet. A lot of the time people are just raising with junk hands hoping to hit the flop hard.

When the flop came 8A4 rainbow, with such a dry board, those who raise preflop with like AK, AQ or any A + random will definitely bet the flop. I personally feel that only AA will check behind and moreover you are in position to him, so only AA will check behind to induce a bluff on the turn.

On top of that you know that he calls preflop and c-bets so light, and he knows that you know that too, if you have a strong hand you would probably raise bigger and cbet big on the flop to get more value out of him. I think he probably feel that you are weak when u did a min raise preflop and check the flop and min raise a acouple of times when a 6h comes on the turn. And I think for his action, he is representing so strong by remin you back. Anyone with a big hand will probably ship the whole stack in on the turn. On a 8A46 board with 2 hearts, the nuts at the point of time can only be 57 but there is a back door flush draw too. With a big hand will you do the min raise here and there? even if you have like a set of A will you do the min back twice? I mean I will not do that.

I personally feel that on the turn that guy must have 57 or 5h7h or A with a runner flush draw or hit a set of 6s there to be able to bet and min raise your min raise so many times.

Therefore i think regardless what comes on the river he is shipping his whole stack in. if you do not intend to call his river ship then you should not call the last min raise.