Pocket pair with single overcard

Wanted the advice of others with far more skill than myself. I played poker for years in the infancy of online poker (and poorly I might add) but wised up and read a few books (Sklansky) and tightened up my play. I know I still have a LOT to learn still. I play mostly MTT's now cause I love the smallish investment (stick to $50 and under) and the joy of playing for 2 plus hours.
My question is how would you play pocket pairs vs a single overcard?
Overview: I'm on the button, p1 and p2. Pocket 9's. I preflop raise 3x BB and get two callers, one I'm reading as a loose player (p1). Flop comes 7,3,J no flush draw. P1 checks and P2 goes all in with his SS for approx 4x BB. Hesitated and eventually folded the 9's. P1 calls and shows A7 and P2 shows pocket 8's.
Did I make the right move? Anything I could should have done differently? Thanks in advance for any and all feedback. This is one that has me stumped. I can understand getting knocked out with my AKs to an AQo when a Q hits on the turn but this one has been bugging me for a bit.

whats your stacksize? depending on how many BB you and the other caller have this may be a shove pre, As played i would call in this spot as the hands that we beat that he is shoving 3xBB with (virtually of them) only contain some that have us beat but not enough to make a call incorrect, would probably reshove to isolate him.

Obv call. If you're 3x raising you should have a stack thats decent enough to absorb a 4x all in. If calling and losing is going to do critical damage to your stack you should've shoved pre.

Not sure why villain is calling pre instead of shoving (if sitting with 7bb's in BB)?

Might be a poorly thought out attempt at a a stop and go. In any case, what do you think the opponents' ranges are given that both called pre-flop? And what proportion of these ranges includes a J? The point here is that all overcards are not the same in terms of the likelihood they hit the opponents' hands.

Not really any advice but Imo, there is no shame in folding a winning hand...Only in calling with the worst.

My one piece of advice would be to pay attention to stack sizes more. Also, with 2 limpers before you, raising 3xBB may or may not be the best tactic, specially if someone with a short stack is limping in. It would have been better to raise more and isolate the shorty, or to just jam it and take the 3.5 BB's out there already. It really depends on stack sizes, but based on the information you provided, it's a shove here. Most likely would get P1 out, and iso P2 for a cheap race of sorts.

No shame in calling with worse either. We only need to be right 23.5% of the time to justify this call. That's presuming antes aren't even in play. Then even if we call bad we still have outs to a set so 8.42%

Agreed. you really need to know more about how the table is playing. But your raise with 3x bb on the button basically can easily be seen to both limpers as an attempted steal. Plus once short guy called half his stack off. He was obviously already planning a stop-n-go. So what he did you had to expect. Then the only question is since p1 checked that basically gave you a green light to go over the top.But you really need to know how the players were playing.

This.
If a short stack limps i am putting him all-in preflop, and with good PP.
Calling his all-in would of been fine to do. Mr SS should of shoved all-in preflop, being that short.
It would help if we had the stack sizes.

the problem here is that you didn't know how to play after the flop if
nothing special happened.
Use the time before acting the first time. This is my advice.

I think what they're trying to say is to have a plan going into the flop. Not to just call and see what happens. Have an idea of what you'll do if x happens. As for the hand. if 4x bb is big enough for you to fold, I woulda just shoved pre. No doubt a call from here, got the odds to call it. If he had more chips though and he made a bet instead of shoving. It's a tough one. Happens to me a lot when i get JJ or QQ and a K or A falls on the flop. You just gotta think back to hands played before and to how they played it up until then. Typically. If I can find any reason as to them possibly having the overcard, I'll fold. I'd rather lose a 4x bb bet then my whole stack. Sure sometimes they are gonna be able to shove you off when you had them beat, but if you feel you're beat, there is nothing wrong whatsoever with laying it down. One of the best things I ever heard in dealing with tournament poker was if you can wait for a better spot to get your chips in, then go ahead, lay down the pp, and wait for your golden hand to come along.