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I don't know what casino this is, but usually at these stakes "seem[img] solid" is not standard. Rebuying preflop should be. Maybe this a 50 bb buyin game or something though.

I usually open limp hands like this and fold to the preflop reraise as played. Also fold to the flop raise as played - live players do not usually know Dan Bright theorem (AK is the nuts). So I think he has something that beats AK, and most of the hands in his range that beat AK also beat 77. Dump it, and don't donkbet either. You'll probably get better advice in the full ring forum.