Bizarre hand culminates in troubling decision

Sorry for the lack of proper hand history, but this one is almost more interesting dramatized.

I was just enjoying a tight/passive afternoon game at 25 NL. I say "enjoying" because at least once in a while, and usually on the weekend, I like to kill half an hour by finding a table full of weak players and just playing their game along with them, but slightly better. It resembles poker, but it's not so stressful - so if I'm having a lazy kind of Saturday or Sunday afternoon, that kind of game can be perfect for my mood. It also works well with my home internet connection, which is shoddy - if a connection drops in a game with few big pots, it doesn't bother me.

Anyhow, the table was full of pushovers and despite myself, I was stealing a lot of pots whenever I had position and someone was betting weakly. The ol' instincts kicking in. On this hand someone limped in front of me, I limped from the button with Kd4d, small blind folded, and big blind checked. There were only four of us playing. The pot now was 85 cents.

The flop came out Kx 8d 6d, which is my dream flop when I'm playing suited crap. BB min-bet (.25) and UTG folded. I was getting ready to raise when my connection dropped. I started clicking away impatiently and when it came back a few seconds later, it appeared that I called instead of raised. Oh well, at least I didn't fold this promising hand, eh? The pot was now 1.35. Meanwhile, small blind AND UTG left the table, so we were down to heads up play. I checked the "deal me out" box.

The turn card was already out and it was an offsuit 4, giving me two pair to go with my flush draw. BB now bet $1, and I decided to find out if he was serious. I raised $2... and he pushed for another $19.

Crap. I had him covered, and I felt like I could be ahead - and even if I wasn't, it was a hard hand to drop with probably 11-13 clean outs even if he was ahead of me now. On the other hand, this is not the kind of hand I like to play when I'm just killing time; the table was breaking up, and I'd rather leave ahead than stuck $15; and this guy was generally a pretty meek, tight player.

What to do? Would you call?

i think you have to fold because of how you described the player types. weak players dont really push AK (or something like 86) there.

What you are describing seems to 100% fit 57 filling a straight. At least that's how people (like me) play hands like that at those levels.

Fold.

I'd be more inclined to call if it wasn't such an absurd overbet. Given that he's a timid player going all-in after this action, and the extremely poor odds you're getting with a dubious two pair, folding is probably best, even with your redraws. 5-7 seems like a fairly likely holding.

It's 25nl, so this is an easy call.

Thanks for the responses, guys. Here's the thought process I went through:

In favor of folding - a straight draw had hit, and it was quite possible that he just made a straight with 57. It was also possible he min-bet with two pair (K8, K6) and then stopped slowplaying it on the turn when he saw he wasn't going to get much action. He could even have checked a middle pair like sixes before the flop and then flopped a set, which he was initially trying to slowplay - although usually this type of player checks every set they flop, rather than min-betting.

In favor of calling - he could also have been slowplaying 86 and just gotten outdrawn. Meek though he was, his type of player still gets married to two pair way too often. He could also have fired out that min-bet with a hand like 84 or 64, and just made a worse two pair than mine. He could be playing back at me with a marginal hand like one pair or a draw because I had been stealing from the table, and him, quite a bit. And finally, he could just think I was stealing because it was the obvious "last hand before the table breaks up," and was trying to go out on a bluff.

I weighed my options, finally decided that I couldn't definitely put him on a hand that beat me, and called. Results:

River was a non-diamond 2 and I won the hand unimproved. Unfortunately, this definitively broke the table up, and since no next hand was played, Party never displayed this hand in the history, so I didn't learn what he had. I may request it today just out of curiosity.