Value Raise or Donk Play?

[Wheatsauce]

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I put him on weaker than top set, maybe even as weak as AAxx unimproved, most likely two pair. Didn't put him on any nut draws

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I don't understand your read here...if he is min-reraising he will almost always have big hand (unless he is a complete donk, which was not stated in the OP), he wants you in the pot. I would say at least nut flush draw with some sort of wrap, with top set very likely also. Just call and see what the turn brings. You have position on him, no need to negate that advantage by going all in.