I'm seeing this line a lot lately and haven't come up with an idea of how to deal with it. Usually when people lead heads up on paired boards or low boards with smaller bets of half the pot or less they are either probing for information with very weak made hands or just assuming you missed and trying to get a cheap fold. I tend to raise those bets with ATC and get folds a majority of the time. When they lead for more, either full pot or close to it, I'm not sure how to respond.
I think leads are often strong in multiway pots where they might assume I'm less likely to cbet, but HU when I'm in position they have to assume I'll fire a cbet most of the time, so why lead? What kind of range do we expect people to have when they take this line? I know it depends on the villain, but I'm running into this a lot and I want to get some idea of a general range for an unknown doing this at these limits.
Bovada No-Limit Hold'em, $0.25 BB (6 handed)
saw flop
MP ($56.79)
Hero (BTN) ($33.96)
Preflop: Hero is BTN with A

, Q

fold,
MP calls $.25, fold,
Hero raises to $1.00, folds,
MP calls
Flop: ($2.35) 6

, 6

, J
(3 players)
MP bets $2.35,
Hero ???
No solid read yet on MP, but he seems kind of fishy since this isn't the first time I've seen him limp call from early position. I have to think I have the best hand here a fair amount of the time, but I don't like just calling this. If it isn't a bluff I think a lot of his range can be small pocket pairs, but I don't know if he will fold them to a raise and I don't want to build a large pot and face tougher decisions on later streets.
As a default, what's the best way to interpret this line and respond to it?