I have an Arkel Utility Basket Pannier which only comes as a single, left-side mount. It is a BIG pannier. I have often filled it with a ton of stuff, OK, not a ton, but a heavy load, and never noticed a bit of difference, even riding no hands. Your body automatically compensates for such things. The balance can cause a problem if you try to use your kickstand (if you have one). Two or three times I have stood the bike up fine with heavy load only to have a puff of breeze blow it over. Now I know in such situations to place it right up against a tree, building, fence, etc. so it can't fall.

I stumbled across the Oyster Bucket panniers a couple of years ago online and came close to buying some.