You could reraise the flop here. As dennis said, usually a 2x bet like this is a rookie trying to act tough. Maybe push it up to 3.5 and see how she goes. This would probably be my line.

If you're more conservative you can call the flop, as you did, and bet strong on the turn. Which you didn't. Bet 3/4 the pot and make opp commit or get out.

Your entire betting line here just screams "weak and will be pushed around," which never works too well.