I likely would have bet it a little less ($30-35) or bet more ($70+) but not saying that it would have been the most EV+ play. In my head to bet smaller would just make it easier to c-bet or check fold my Kings if an A hit which by now you have to think at least 1 person has. You do open yourself up for more callers but could also increase size of pot this way (but not nessesarily EV... But might make it easier for you to fold when beat as well). If I bet more I would just want this pot here and now (pot is 10% of your stack) or get ready to put all of my chips in.
I have been playing a lot of short stack Live 1/2 NL and it is easy to get handcuffed in pots where you dont have enough stack behind you to play effectivly. I feel like this hand has that potential.
By 3 Betting You acomplished what you wanted by ISOing the HJ. Because you are going to be out of posiiton I can see the need for 3 betting to at least $40 so you dont have 2 villans behind. So if all goes as planned HJ would need to call $31 in a $60 pot. If he has Ak, AQ, or 99+ (except for AA) you are looking good and can give him odds
that he thinks he is good to call.
IMO the only real problem with the $40 3-bET is you are risking 20% of your stack before you see the flop. This just limits your ability to make moves post flop play as the pot is going to be only 1/2 the size of your stack after the flop.
When A comes out on the flop it depends on Villan and how he has been playing. Stats look like you may be able to get away with a C-Bet here and get villan to fold if he does not have an A. Also, he is not particularly aggresive so maybe you check to try to see a free card Both should be played depending on Villian I would say ideally 70/30 with the C-Bet to check on this flop. The tough thing is by putting in a $45 C-bet you have now put in 40% of your stack in a pot that if called or raised you are likely a big dog. I would imagine that this was a factor of why you did not C-Bet here.
So overall I would just say be aware of your pre-flop bet size relative to your stack size when 3 Betting. The $40 3 bet was good size for the pot just IMO rough on your stack. However 75% of the time in this situation you dont have to worry about the A coming out on the flop so overextending pre flop would not hurt as bad.