Floating HU: Turn Plan?

[KLJ]

I've been thinking a lot about this and haven't really figured anything out.

Say someone opens ahead of you and you call in position (maybe because the opener sucks, maybe because there's some donks behind, who knows). Unfortunately, everyone folds and the pot is heads up.

The flop comes, your villain cbets, and you call in position for whatever reason.

The turn is a relative blank and your villain checks to you.

1. Say your range is something like this:
{medium strength pair, draw (assuming you didn't raise), air, sometimes a strong hand (maybe for balance)}

What are you betting and why? what matters that I haven't told you? (position of opener, range, aggression, etc)