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I'd fold. The hands you beat are JJ-66 (36 ways). The hands that beat you are 55,44,33,54,43,A2 (43 ways). The times he has 65 and bets probably cancel out the times he has 67 and bets.

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You are giving incorrect weight to 54, 43, A2. We should at least assume that villain is only playing suited variants of these hands, if we are going to consider them with the same probability as the overpairs. I don't see a solid BB calling here with A2o, 4/3o, and 5/4o very often.