What's The Proper Play Here?

[Diboss]

I've noticed that I tend to play my strong hands too aggressively, to the point that I sometimes end up putting my whole stack in the middle, which isn't bad in itself, but I feel maybe I should slow down before.
This is a made up hand, so let's work with it, BB is $0.50:

As Qh on the button.
3 limp to me and I raise to $3, the BB and MP call.

$9.75 in pot and flop is Ac 9c 5h.
Checked to me and I bet $5, both call

$24.75 in pot and turn is Th, checked to me again.
Now this is where my aggression would get me in trouble, I've been likely to bet maybe $15-$25 here, figuring someone on the flush draw and trying to get them to fold. Is this a proper play? or should I just check here since no really smaller bet is likely to get anyone to fold. I really need help on this one folks, I'm a winning player overall, but I think this may be one of my leaks.

Some of my thinking in this kind of situation:
55 could hit his set, wouldn't have folded to the best.
A9 or AT could two pair, and trust me, the people I play with will call that preflop raise with that.
Xc Yc is the most obvious here.