What is causing my TJ body to sway?

Should the Jeep be hard to push down on the bumpers?
Your fighting the springs at that point to. A way to test them somewhat on the jeep is to push it down and see if it ocolates more than once. Better to test the shock off the jeep though.


There must have been a time
when we could have said no.
 
What is a good shock to replace them with?. Locally I can get Rancho's, Pro-Comp, Skyjacker, and Tough Country. I'm not going to be doing any serious off-roading with it
Only three bolts hold the shocks on, at least remove a couple to test them as I recommended above before buying new shocks. No need to jack the Jeep up, the shocks can be removed and replaced with the tires on the ground. If you find they're bad, I'd go with Rancho RS5000x shocks. Don't get confused with the older RS5000 which is a horribly stiff shock when mounted on the Wrangler. It's the RS5000x that I'm recommending.
 
I removed one of the rear lower shock bolts and it takes a little force not much to move the shock in and out. It stays in whatever positon I put it at but not with very much force. Easily done with one hand
 
I removed one of the rear lower shock bolts and it takes a little force not much to move the shock in and out. It stays in whatever position I put it at but not with very much force. Easily done with one hand
That definitely sounds like a weak/bad shock. An RS5000 like you have should be very stiff/hard to push/pull in/out.