I am in my late twenties and have been on the table for 30 minutes and won a couple of pots without showdown. Villain is an old gentleman and the only hand he played was as follows: He completed the small blind after two limps, big blind made it $10. All 3 players called. On the A35 flop he checks and big blind leads for $10, the player after bb raised to $20, button called and villain made it $110. Everybody folded. He claimed to have a small flush.

OTTH. Effective stacks are $300.

It folded to me and I opened to $10 (standard for the table) with 24 on the hijack, villain flatted from the button. Everybody else folded.

$ 20 after rake
Flop Q6Q

I bet $15 and villain flatted.

$ 50
Turn A

I bet $25 and villain raised to $60. What should I do? I think his pre flop calling range is broadway cards, pocket pairs and (maybe) suited connectors.
I discount suited connectors because I think he would not call with them if he does not think the pot would be multi-way. Given his tight image, on the flop, he is probably not calling without a Q, a pocket pair (including 66) and hearts. I think his raising range on the turn is 66, AQ, hearts or strangely played Qx (maybe QK?). Is this an easy fold?

LOL... you know everything from this point forward becomes "on your own head"... really easy fold pre.

As played, flop and turn bet seem standard to me. Your analysis of villains turn raise range seems reasonable to me. One thing to note was that on the previous hand you saw him play... he made a very big bet on his (reported) made hand. This time it's a little undersized. But that might just be out of respect for a possible Qx.

I think that, at this price, I'm calling and checking back the river with a view to call a small bet and fold to a bet > half. But a fold wouldn't be horrible either.

Even if we are 150 BB deep this still doesn't justify raising 42s, just fold preflop

Fold pre. As played I'd call and b/f $60 on non heart River unless board double pairs.