Originally Posted by BLieve
In situations like these, do I bet or not?
Allow me to rephrase your conundrum for you:
On the turn, you're feeling pretty certain that your hand is in one of three categories: Crushed (by a set or somewhat unlikely JJ+), crushing (versus a smaller pair) or in decent shape versus overcards. You're out of position. Is there a reason to bet?
Yes there is: For value. You can bet/fold the turn if you think villain is very unlikely to raise with worse than what you have. Combinatorically, your opponent's range is of course heavily weighted towards hands that you beat, and unless you have reason to believe he's floating the flop with the intention of bluffing the turn if checked to, betting makes the most sense - but only if you beat his calling range.
How do we accomplish this? By betting small. You'll induce loose calls from small pocket pairs that feel they're getting a good price, and you'll induce folds from overcards that probably shouldn't fold if they knew what you had. It doesn't take much for him to fold ~15% equity with a hand like QJ and out of position that's not a bad proposition for you. So bet less than the $7.50; probably more like halfpot or even just $4. If you get raised, you lose a smaller amount than with your bet size, and you should get called more often by weaker hands than with your larger bet size.
So, in my mind, this is not a question of whether or not to bet, it's a question of how much to bet. And I vote "small."