TPGK, Nut FD-- how fast to play it?

I've taken some time off from playing given the US shakeup so I'm a bit rusty (not to mention not being very good in the first place). But here's a BoDog hand from last night as best as I can reconstruct it:

25NL
9 handed

Hero has ~100BB, villain covers. No reads
Hero: on the button

PREFLOP:

3 limpers, Hero raises to $1.7, SB calls, two limpers call.

FLOP (pot ~$7.30):


SB bets $0.25, two callers, Hero raises to $5, SB calls, 2 folds.

TURN (pot ~$17.80 and hero has about $17.25 left now):


SB bets $0.25

So my question at this point is it better to push here or just bet $10 and get the rest in on the river?

The action suggests a FD or weaker A to me (or I'm getting goaded into a big pot by a thinking player) but I never know what to do with these minbet leads into big pots.

I may just call it, his play makes little sense but the pot is very big, if he is drawing to the flush draw you have him beat.
At this point I would try to get to a cheap showdown unless I improve on the river, If I dont improve I call a reasonable bet.
Villian may have A9 or a set, his call on the flop worried me a lot

I'd say push him all in here, you are ahead most the time. If he has a set/AK and you dont hit, unlucky. But if he has a Weaker ace or someother shoddy hand or flush draw you got him beat. Just push and hope for the best, get a nice read for later too.

Who is villain?

Sometimes I push sometimes I call depending on who it is.

If its someone whos normally quite aggressive then I just call.

If its someone whos normally loose/passive / clueless then I probably push.