[Big_Jim]

I think typical villian, that you describe, has a hand range of about:

A9s+ ATo+ KJs+ KQo 99+ + some even worse hands

(Feel free to dispute this)

Based on a few pokerstovings using the above range, I found:
AKo
equity (%) win (%) / tie (%)

Hand 1: 39.1756 % [ 00.34 00.05 ] { AA-99, AKs-A9s, KQs-KJs, AKo-ATo, KQo-KJo }
Hand 2: 60.8244 % [ 00.56 00.05 ] { AKo }

QQ
equity (%) win (%) / tie (%)

Hand 1: 35.7790 % [ 00.35 00.01 ] { AA-99, AKs-A9s, KQs-KJs, AKo-ATo, KQo-KJo }
Hand 2: 64.2210 % [ 00.64 00.01 ] { QQ }


Go much worse than that, and it gets real borderline...
JJ
equity (%) win (%) / tie (%)

Hand 1: 43.1096 % [ 00.42 00.01 ] { AA-99, AKs-A9s, KQs-KJs, AKo-ATo, KQo-KJo }
Hand 2: 56.8904 % [ 00.56 00.01 ] { JJ }

AQs
equity (%) win (%) / tie (%)

Hand 1: 44.4713 % [ 00.40 00.05 ] { AA-99, AKs-A9s, KQs-KJs, AKo-ATo, KQo-KJo }
Hand 2: 55.5287 % [ 00.51 00.05 ] { AQs }


Of course, this is hardly entirely accurate, but this is based on my experience on short stacked donkish tilting players.