[wiggs73]

Hand 1, I can see him playing a king like this, but against the villain you describe, there is also a good chance he has a 9 or is bluffing. I'd probably check/call. Money is going in against a king regardless, probably against a 9 regardless, but you take away his chance to bluff again if you bet. I don't know how often he calls with worse, but since most small pairs got counter fitted on the river, I don't think he's looking you up all that often if you bet. If stacks were a lot deeper, bet/folding the river would be an option, but it isn't with these stacks.

As for hand 2, I'd just shove preflop since limping isn't at all out of the ordinary for villain. It would take a certain kind of dynamic for me to check, something like a villain who almost never limps, who is competent, and who would generally expect you to push a wide range in this spot. In such a situation, I'd be leery of a trap, but based on the info you've given I think villain is most likely not thinking anything more than "ooh 2 cards, cheap flop."