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When he checks to you, he's pretty much saying he has 10s Js or Qs unless he is trying to slowplay a huge set or something.
Top 30% of hands includes {55+,A2s+,K5s+,Q7s+,J8s+,T8s+,98s,A7o+,K9o+,Q9o+,J 9o+}
That seems like a pretty wide range but we'll go with it. On teh flop, he's checking all Pocket Pairs because he puts you on an ace or a king at least. He's also checking missed flops and maybe AK. Purely based on his range your a ahead of his range 43% of the time so this is a check-fold postflop. You probably should have shoved preflop as your ahead of almost all of his range as a 72% favorite so you wouldn't be faced with this situation.
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