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I agree that your opponent rarely has a big value hand here. With a big hand in a three way pot as the caller it would make sense for him to wait and see if someone else is willing to put more money in the pot before revealing the strength of his hand.
I do like the squeeze play that OSUBuckMan makes with 9d7d in this hand. I also like your call. In my opinion this hand is a good example of a situation where it is correct for both the aggressor and the caller to get all the chips in on the flop. A sufficient amount of chips have gone in already that hands as strong as 9d7d and 9s9h are committed to this pot.
From OSUBuckMan points of view he is making a 2x shove vs hero, but less than a pot sized shove vs EagleAces12345.
In order to analyze the hands I put both OSUBuckMan and your hands into an equity calculator. The plots attached show the equity of all hands vs the hands you and your opponent actually had. I made separate plots for combos with/without a diamond.
The pot is 7885 when OSUBuckMan chooses to go all-in. EagleAces12345 has 5634 left and OSUBuckMan 19597. Hero covers both.
Outcome 1: EagleAces12345 calls, FiveByFive folds
OSUBuckMan invests 7610 into a pot that becomes 21129. Required equity for OSUBuckMan is 36%, i.e. EagleAces12345 needs to have more than 64% equity for this to be loosing push for OSUBuckMan. As we can see from the plots in the top row there are very few hands that EagleAces12345 can have that has a larger equity than that. A hand as strong as JdTx (trips + backdoor flush draw) is break even from OSUBuckMan point of view.
Outcome 2 EagleAces12345 folds, FiveByFive calls:
OSUBuckMan invests 19597 into a pot that becomes 45121. Required equity is 43%, i.e FiveByFive needs to have more than 57% equity for this to be loosing push for OSUBuckMan. As we see from the plots in the top row there are still quite few hands that meet that criteria.
The bottom two plots show the equity of calling with 9s9h vs various hand your opponents can have. Hero needs to call 17621 in a pot that becomes 45121, requiring 39% equity (i.e. only loosing when opponent have more than 61% equity). As we see from the bottom plots there are mostly made hands that have that much equity. A lot of the drawing hands that the opponent could have has lower equity than that, making 9s9h a good call.