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Blinds are 25/50. I am fourth to act pre-flop with a pair of 8's.
That's not enough information. You need to give the stack sizes. They matter a lot.
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My thinking was the guy who initially went all-in had to have a bigger pair than me. He saw me raise, two people call my raise then went all-in anyways.
Flawed logic?? Yes?? No??
You overlooked that the player who pushed had first overlimped.
Sometimes a limp-reraise represented strength. In very low stakes game, it often does not, perhaps that the player is unwilling to play the mediocre hand out of position postflop, but doesn't want to fold. However, a strong limp-reraise is usually done in early position before anyone has entered the pot. Picking up the blinds is a bad result with AA or KK, and if players have been respecting early position open-raises, then it may be worth trying to limp-reraise. However, it is much less common for someone to limp with a strong hand after another limper. In that situation, few people would fail to raise with AA.
However, it depends on the stack sizes. If the push was large in relation to the pot, it is more likely to be a big pair. If you were getting good pot odds, then the push represents less strength, and you might want to call even if you felt that it is very likely that you are up against a higher pair.
In general, don't worry if you lose a small pot when you were a tiny favorite with a medium or low pair. It's only when someone shows you 22 or A3 that you should regret folding 88.