Bet increase with winning hand

When you most likely have the winning hand, and have been betting 3xBB with no re-raises, how much would you increase your bet on the river? You want a call, and don't want to scare the caller off.

it's not that simple. Positions are important, what villain's range look like, previous actions, some history, what kind of your opponent is, board structure etc. There are too many factors to answer your question. Sometimes its 30% of the pot, sometimes 50%, 75%, 90% or even 150%. Every situation is different.

If I had the nuts, I'd cheat. I would bet half the pot - it's very similar to a bluff and the opponent is likely to put his entire stack on the table!

Depends for me on the stack sizes, compared to the Pot.

If u have the nuts, go for it.
It would be around 70% in average cases.

But you also have to consider the board and what he can have. And then size your bet.