Putting this in NSFW tags. It might sound cruel, but the cat likes it.
Err...hmmm...I'm assuming you don't mean that you pick the entire cat up off the ground by her tail??
Two things:
1. Hello arthritis!! When she is older this is very likely to cause her problems
2. Cats also purr when they're in pain or extreme anxiety/stress, not just for pleasure. Are you sure she likes it??
Maybe just stick to massaging her? (which is of course extremely beneficial!!)
My cat Smoodge plays fetch. He's quite adept at it
My cat Toby has a fetish with socks. Every night when I first get in to bed he will pull out a sock that he's stashed somewhere (probably under the couch in the loungeroom) and bring it to me in the bedrom, meowing the whole way as he brings it up the hallway as if he's caught it and is offering it to me as a gift

It's absolutely hilarious. He does it every night without fail, and sometimes during the day when I'm at the computer he will do the opposite (i.e. bring me a sock from the bedroom).
My dog Cosby is just really smart. It's almost like he reads my mind sometimes. I can ask him to do a new command he can learn it within a matter of seconds. Plus he's just amazing in general. My little maaannnn!!!!
My other cat Sushi is just a cat.....she's gorgeous and all but she doesn't really do anything particular noteworthy.
Same with my lorikeet Buzz, he's a right cheeky little fucker and can be extremely entertaining! But he doesn't do anything particularly special.