[Big_Jim]

You say button is solid, so what hands is he calling with PF?

I'd say his range is probably along the lines of PP 22-JJ, maybe QQ, he would re-raise AA, KK.
AKo AQ, maybe KQ.
And suited connectors

He cold calls your bet on the flop, so what could he be calling with? The only draw is 67s for the straight. Other than that, a cold call worries me. I don't know what he would call with that you beat, other than the draw, and I don't know that a solid player calls this with the draw. If he views you as LAG, then he might be calling with a PP < Q.

Do you usually fire out a continuation bet after you raise PF? What about with 3 people to the flop? What does the slight overbet usually mean, from you?

After he cold calls the flop, I like the turn check.

On the river, I would probably value bet about 2/3 of the pot (300), and fold to a raise. I like a value bet, but only if both of the following are true: a)we don't view button as capable of making a big bluff on the river b) We are very sure that button views hero as very LAG. By showing weakness on the turn, you make it possible for him to call with any PP that he called with on the flop.

If these assumptions are not met, I would check call a decent river bet. (Up to about 300)