Welcome to Just Answer, I will do my best to help you solve your problem
You tighten the handle by tightening the allen screw on the handle. Is something else loose? is the allen screw stripped?
Not stripped, just doesn't tighten. Could be that I am afraid to try try too hard a break it.
It could also be seized up. You probably won't break the screw ( you could strip it) and it's the only way to tighten the handle. Try backing the screw out first, then tighten it down.
I just looked at the faucet again to make sure I am correct in my assessment of what is wrong. Now, I don't think I was correct. When I grab the entire unit I can move it a little up and a little sideways. I feel the whole unit is is loos.
then you will need to tighten up the the nut at the base of the faucet under the sink
I am not good at these these, but I will try to explain. I don't see a nut I can tight with a wrench. Remeber, I need very detailed help.
if you want "very detailed help" I need the model of the faucet. There is a nut under there. You may not be able to get to it with a conventional wrench. These faucet often come with a deep socket to tighten the nut.
there is a round metal thing (sorry) that I can turn clockwise and counter clockwise. couls that be what I tight the base with?
I believe the model is a delta signature... single handle pull-out faucet.
your description is too vague, the round metal thing could be anything. Guve me a minute to see if I can find the spec for the Signature pullout
wow... now you're starting to give me the impression you're pissed. Forget it. I'm also not paying you.