Hi everyone.  New to TPE and I figured I'd start off with an odd hand I ran into in a live $300 event at The Bike in L.A.

Blinds are 100/200 with no ante.  MP2 limps, I limp in the Hijack with 78, SB limps, and the BB checks.

Flop is 577.  SB leads out for 450 into the 800 pot (SB has about 5.5k behind), and BB shoves for 24k pretty quickly.  MP2 folds, and it's on me.  I have about 18k, and my read on the BB so far has been a fairly tight passive player.  I've rarely seen her bet, content to check-call hands like AQ on an A high board.  And when I have seen her bet, it was in the “normal” betting range.  There haven't been any crazy plays like this at the table, and it is definitely the biggest pot at the table at this point by far.  Here's my thought process:

If she has a 7 here, she can have any kicker since she just checked in the BB.  With my 78, I beat 76-72 (minus 75 of course), lose to 79+ and 55, and tie 78.  From a purely mathematical standpoint, I should fold here since there are more hands that beat me than I beat.  However, I can't assume the BB has either a 7 or 55 here 100% of the time, which may tip the scales toward calling.  On the other hand, I only have 200 invested in this pot and could easily fold, leaving myself 90 BBs.  But why would someone with a 7 or 55 take this line in a small 4-way limped pot?  99% of the time, the BB will just rake in the measly 1250 pot.  With the crazy all-in on the flop, I find it difficult to put the BB on a hand or even a range of hands because it's impossible to go through the thought process of someone who isn't thinking.  The only real conclusion I could draw was that the BB was a bad player…I just didn't know to what degree.

Thoughts/perspectives are appreciated.  Also, I don't know what the protocol is for revealing my decision, so I'll hold off and possibly post it later.

Thanks.