When to give up when you miss

[Man of Means]

Preflop starts a chain reaction of having to bet to win the ever-increasing pot. This happens sometimes, but realizing you're out of position, you might consider limping, then trying to pick up the small pot on a dry flop. But raising isn't out of line.

If we can quantify how tight BB is, the hand is easier to understand.

Check the river. Your bet will get called by a pair very often, and only serves to block a bluff attempt on his part. If he is passive, he is not likely to bet the river without a pair. Sometimes you'll get a free showdown and win with K-high.