Do all lightweight large TT's tow terribly, or just ours?

Put another washer on your hitch, drop the TT tongue an inch, and put some more tongue weight. Do each of these and check in between. I'm betting the extra washer will make a huge difference.

Make sure that your Burb tires are inflated correctly for the load, and consider going up another load range if you are close to the top.

Make sure the TT tires are inflated correctly for the load (usually max pressure.)

Regardless, it's not going to tow like a 5th wheel, but it shouldn't be squirrely.