Player B has AA.
In this real life scenario, the tight aggressive player does not normally go all-in preflop with any thing but AA or KK, and AA is more likely.
If you said AA, then give yourself a pat on the back. If you said KK, then close enough in this case. If you said anything else, then you probably thought about it way to hard and talked yourself out of the obvious answer. In my experience, the obvious answer is usually correct.
Why did Player B bet so much? Player A has shown himself to be loose-aggressive. Loose aggressive players will often talk themselves into calling hands they should fold. Player B bet so much because he knew that Player A would interpret the over bet as a bluff, because that is exactly the kind of play he himself would make. This is exactly what happened - Player A called with QQ, putting all his chips into a pot in which he was dominated.
