I agree in principle with Hirondelle, and apparently I agree in practice, because thinking back I've remembered a number of heavy and/or awkward loads I carried on a bike and/or with a bike trailer:
Pier 1 was having a sale on plates we rather liked, so we purchased full settings for 12 and I towed it home in a trailer (it was heavy ceramic, so maybe around 50 lbs? It was enough to pull me back a bit, starting on a hill).
Similarly, I was at our local hardware store on a bike and they were selling off their last few 6 foot iron trellises, which we needed for growing roses but hadn't wanted to pay for. I bought their last two or three and rode my bike back home holding them in my right hand (the left hand being used on the front, i.e. important, brake, obviously) out away from the bike.
We've started taking things to potlucks separately from their serving dishes, so the serving bowls can go into a backpack and the food can be in a closed container, and the two don't have to be kept horizontal in transit. That really eases the burden of getting yummy things to other places.
I think the biggest, though, (in concept, as well as fact) was when my 5th grader decided to play trombone in school band class. We bike commuted, and I suggested he consider a smaller instrument. Nope, trombone. So his dad and uncle put a rear rack on his bike, and rigged up a trombone support that had a folding horizontal piece where the bottom of a pannier would go (so it could be folded out of the way when not in use) and the kid biked with a trombone case three days a week for 5th - 7th grade. (At that point we acquired a second one, so the nice one stayed home, generally, and the less nice one stayed at school, generally.)