Lots of good answers already, but here's a real world example of why not to use an extension:
Years ago as a "green" tower, we got our first RV. It was a 16' or 17' Shasta. I pulled it with my Jeep TJ. No trailer brakes, no WD hitch, no sway bars, nothing but the receiver hitch - like I said, I was new to the world of towing. It seemed like the best of both worlds, I had a TV that could go anywhere unhooked, and it still fit all of my family in it. (I added a third seatbelt in the rear).
It pulled the trailer ok. Going up an incline at highway speeds was not possible. about 40mph was the best I could do unless it was relativley flat. Stopping was fine when I allowed myself plenty of time to do so. Stopping in a hurry proved to be scary when I had to do it
What does all that have to do with an extension? As if I wasn't already pushing the limits with that setup, I wanted to take my TY350 with me also. I bought a hitch extension and fabricated a motorcycle carrier out of heavy U channel steel. (Not the cheap lightweight ones you can find premade today. This thing probably weighed 50 lbs on it's own) I bolted that to the extension, loaded my TY and then hooked up the trailer. The trailer sagged, so I pulled the 2" drop ball mount and reversed it. That seemed to be the ticket, I was back to level.
Off we went to Lion's Head up at Priest Lake
. Pulled fine (read above) until we got there. Right before we turn off the main road, there is a bridge. At that time there was a huge pothole. I was following some friends, and didn't see it until we hit it at too high of a speed. That was the first straw in breaking the camels back.
Now we turn off the main road to the right and go up some old logging roads. We're not camping in the camp ground at Lion's Head, but up in the "wild". This road is not paved, and every so often there are berms across the road to aid in water runoff. Going over each berm was one more straw added. Going over the berms, the trailer sagged a little more each time until when we reached camp I was dragging a furrow thru each berm.
Picture the letter "V". One leg of the V was the trailer, the other leg was the Jeep. I'm sure I was already beyond the towing limits of the Jeep with the setup minus the extension and motorcycle carrier. The extension pushed the weight of the trailer to far out.
The receiver hitch did not break, each bump just bent/pushed it further and further down. When we reached camp, we were able to remove the motorcycle, then used a farm jack underneath the extension to lift the point of the "V" up, reversing the weight and bending the hitch back up and into place (well mostly
). I removed the extension, had some friends hook it to the back of their motorhome and haul my TY home for me. I never used the extension to tow again. I do use the extension/motorcycle carrier on the Jeep to take my bike up in the hills, but nothing else