Only my opinion but I'm almost sure he has a king, not even a Jack, his min bet is to see if you have anything/induce a bluff raise. Once he min re-raises the turn I fold and run...
I think the yeti-theorem can apply, but these cards are such a big part of your range that he would bet at them, just very small to try keep you in and see if you have anything that might pay him off.
I think I might also test it (the theorem) on the turn but once he min re-raises...§
I fold.
(The min reraise looks like hes 'testing' to see if you 'really have a king' which might make sense if the board was 6886 and he was testing to see if you really had an 8 but not on this board given you were the pfr utg.)