cgconrad004e, It is not your TV. There are lots of variables when it comes to this issue. Loading the trailer might be one. If you remove weight from the hitch as you would by loading heavy stuff behind the axles, you can get into trouble. This usually shows up as trailer sway. Your hitch could be a problem if it is an older one with parts starting to wear.
The receiver on your TV can and usually will wear to the point where the stinger can move around a bit. I had a new '08 Tundra and after about 7 or 8 years mine developed a bit of slop. I noticed it when starting out from a stop as I would hear and feel a "clunk" when the stinger moved back against the pin. I looked into a fix and there are a few out there. The shims mentioned earlier work but they wear out quickly and have to be replaced. There are after market fixes you can find on line. You can also go into a hitch service and they can weld bead into your hitch opening which will firm things up.
Being your typical lazy American, I just got a new truck. Actually, the hitch wasn't my only reason.....:B