I use Wald folding baskets to carry my backpack, lunch, etc back and forth to campus. As far as weight distribution goes, I'm another one who always puts the heavier load (or only load, if I'm just bringing one bag with me) on the right side, because my right food is the one I naturally tend to put down at stops. Once, I had to reverse the weight distribution (because I lost part of the mount on the right side, and didn't want to put much weight in that basket), and then I did feel a bit unstable and "tippy" towards the left. But as long as the weight is roughly balanced or heavier on the right, I have no problems.
When I REALLY had problems were on days that I would ride another bike and suddenly have to go back to carrying all that weight on my back! Once you move to letting the bike carry your things for you, you may wonder how you ever got along before.
'09 Jamis Satellite Femme | stock Jamis Road Sport -- road
'08 Trek 7.2FX | Terry Cite -- commuter
'77 Raleigh Grand Prix mixte | stock Brooks (vinyl) -- just for fun!