If you post a picture of the "above the counter" part of the faucet, I bet someone here will recognize the brand if not the model.
I don't know why I didn't think to post an above shot. . . VERY short sighted of me. And now I'm at work and can't get one. However, this is basically what it looks like, so I think hj was correct that it's a Grohe:
usually it just pulls out, but if that is the type of faucet you have, you would have to remove the hose to tighten the faucet.
I did try just pulling up on it and that worked! But of course I don't have the "special install tool" since I'm not the original purchaser. BUT, it does have 2 "flats" on the sides of the main part of the faucet, so I THINK I'll be able to simply tighten it as shown here:
Let me know if this is a bad idea for some reason. . . . but seems easy enough!
That's not the EXACT faucet i have, but it looks identical except for the shape of the neck and the type of head. . .
Thanks everybody for the help!