My 1999 blazer rear sways when im driving worsens around corners.

Winter doesn't matter, because tires are always measured cold.

1999 Chevrolet Blazer Tire Pressure

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1999 Chevrolet Blazer LS 4x2 · 35 psi · 35 psi · 32 psi · (32 psi). Front Tire, Rear Tire. People also ask

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On a 2006, the towing weight probably split the Sway Bar bushings. The sway bar stops the back from swaying. Could also be shocks as well or both.

Push down on the back and see if it bounces.

Don't drive it further than a local garage/technician or an experienced neighbour. Something maybe adrift in the axle/suspension area and could lead to a crash. Most likely its one or more rubber bushes in the suspension need changing. Check your shocks while you are down there.

Yup

if rear wheel drive check the prop-shaft the universal joints may be loose.

could be rear wheel bearings - they come as a complete assy with brake hub - approx $45 each side - 1 hour per side for replacement. Also replace the rear sway bar links $8 for a set - other than that you could have a bent wheel and or loose rear control arm bolts - remove the rear wheels and check all mounting bolts - I had this problem and my rear end felt like it was shimming when I went around corners - 5 minute fix

A sway bar is a suspension piece that keeps the left and right side of vehicle connected to help with turns. They are held together through sway bar links at each end, which are fairly common to break or rattle over bumps.

Cheap and easy fix, just replace the rubber bushings under the back where the sway bar is held to the chassis. The rubber gets worn and hard and allows the bar to rattle when going over bumps.

a sway bar is usually u shaped and hooks to the body and the tops of the u hook to the axle with links that have bushings. most jeeps dont have a rear sway bar.the panhard bar is the rod that goes from one side of the axle to the body on the opposite side. its sometimes mistakenly called sway bar. it keeps the body from moving side to side around corners. then there are the torque bars they keep the axle from trying to rotate when accelerating.
none of this would be real expensive but if its been lifted a bunch then you may have problems

Have the shocks/struts ever been replaced? The rocking is normally caused by worn out shocks and/or sway bar bushings. When the shocks go, you normally will experience a rollercoaster type up and down motion when you hit bumps (the springs are bouncing and the shocks are not dampening/rebounding properly). If you do not have this up and down rocking, but just sideways, check your front and rear sway bar bushings for wear or damage to where they connect to the frame. If the mount has broken or come loose, it will not prevent the sideways sway. You should also see a sideways lean going around corners.