Steering Wheel Shimmy

Today my 2005 Chevy Aveo LT started a shimmy in the steering wheel at about 50 mph. A definite, strong shimmy. I pulled over and inspected all 4 tires and wheels, and gave each one a good shake. Tires are all great. No loose lug nuts. No uneven tread wear. When I pulled back out onto the roadway the shimmy was gone and all was well. 15 minutes later the shimmy started to gradually come back. I'd appreciate any and all suggestions for what I should be looking for when I jack it up. Thanks to all for your help in the past.

Maybe a wheel weight flew off on a decent pothole. I'd look for signs of a missing wheel weight, when you jack up the car have someone rotate the tires while you watch the inside rim edge for signs of a flat spot. The factory steel rims are known to bend easy, yet cost 65 a piece.. (scam if you ask me)
Your LT probably has the upscale alloy wheels which might not get bent so easy.

lost a weight, brake stuck, low air, tie rod, etc; basic trouble shooting. just all corners up and try to move tire and if wiggles u got troubles

I would definitely check the tire balance

Just another thought - had a shimmy that was caused by a seizing drivers side front brake caliper... as I drove enough it would heat up the brake and cause a shimmy. Replaced the caliper, all is fine.