Postflop play

I would check flop. You have overcards so A or K is ok. Dont have bdfd and Qx is strongly in reasonable SB call range. Dont see real point in betting this combo. As played turn and river is fine.

Depending on the player type we'd have to defend vs. river probe with a hand strong like this (top-pair top-kicker). But since this spot is so underbluffed by the nutpeddlers I can see the fold to be a good play against such. On the flop generally you have to mix up your betting strategy so you want to bet some of the pocket pairs and check sometimes. To find an appropriate way to execute this you'd have to study solvers range to give you a sense of what we would be supposed to be doing. This is how my strategy with pocket-pairs looks like when being MP facing a BB call on a Q♠:Q♦:8♣: flop:

Any :3x::3x: or :2x::2x: would cbet with full frequency (they have the least SDV and benefit the most from getting villain to fold) and the :Jx::Jx: would be a low 25% cbet (they are already a borderline value-bet: Using a randomizer I only cbet those when my first starting hand card is a club. Since Jacks make a big portion of your pocket pairs range from a tight early position RFI, we would have to be more selective witht those). Mid-high pocket-pairs like :Tx::Tx: and :9x::9x: with a frequency around 10% were simplified towards a 100% check-back.

Using a randomization strategy ensures you are betting the right amount of hands out of each category, strictly spoken having a specific type of bdfd itself does not tell the whole story, but as correctly mentioned having overcards generally favours checking (your JJ's become invulnerable to be outdrawn by a highcard). The most important factor out of those 3 when deciding to bet is the rank of our pocket pair.