I've learned to do smaller shopping trips, and I've found that to be OK. There is a tendency to want capacity to carry the biggest conceivable load, but it's really not that important. I buy what fits and save buying the rest for later. I use panniers. When they're empty, they're very light and quiet.

Interestingly, if I have only one pannier, or if I load them unevenly, it's not at all difficult to ride.