In small stakes games, I see a lot of players who limp too wide a range, who then can’t stop themselves from calling a preflop raise. Their $1 hand somehow just became a $7 hand? Rrrokay.
So while you could be behind AQ and QT, you and the board block a ton of those. There is a lot more other stubborn Ax/Qx out there which might continue, as well as other combos with one pair and a straight draw (say, QJ, suited Q9, Q8, TJ, T9, T8) and open-enders/double gutters. I even find plenty of low stakes players who simply can’t release a pocket pair which is totally dominated by the board. Or an Ace-high backdoor flush draw. You want to get value from those, even though once a long while they will catch up...
You might even be behind Q7s and T7s, but do these guys really call $7 that wide preflop?
Unless you have a specific read on these players, this hand seems like a good one to “protect” your continuation betting range. That is: There are going to be many similar situations where you flopped better or worse where you want to bet again. This combo (TP/good kicker) is a solid candidate for protecting that range.
If you get reraised, then a specific read on these players seems even more important and theory starts to go out the window... (Is the guy who limped first the type to take it slow with AA/KK/QQ? If he limped those hands to trap and you made it $7, wouldn’t he re-raise preflop?)
Anyway, I like the bet size. Might have gone a little smaller but only 1-2 bucks. If called, re-evaluate on the turn, which often is going to go check-check depending on whether anyone improves or a scare card comes (such as the board pairing, or maybe a J?).