Sarah raises an excellent point in her comment--I frequently forget to tell you where my fabrics came from. The pink, blue, flowered striped fabric in the grocery bag is from Joann's red tag section, about a year ago. It's a heavier weight, almost canvas. I bought it twice. The first time, I planned to make tote bags with it. The second time, it was to coordinate with other fabrics on one of those toddler chairs (McCalls 9665) that I was making for the baby's birthday (last, um, fall). The chair has been stalled for the last, um, year, but I'm thinking of finishing it for birthday No. 2.
As for the strength of these bags, as Jennifer wondered, the pink striped one is pretty solid. It's also a bit smaller, so I made it with the idea that it would be a "can" bag. I piled about 8-10 cans in there and it didn't seem to stretch too much. The reinforced handles are very good--because they end up being sewn about three times, in three different ways. So I certainly don't think they would fall off on you. The bottom is pretty sturdy, but based on my rather informal test, I wouldn't do more than 6-8 cans in any one bag. But it could definitely hold a mix of cans and boxes and things pretty well.
The bag from Wisdom of the Moon's tutorial might be even stronger, because it uses one long piece of fabric folded over with no real seam along the bottom. So, no seam to handle the stress of the cans, just the fabric itself. I haven't given the bags a real test run at the market, but I am pretty confident in their strength. The french seams that the bags use are also supposed to make them quite a bit sturdier than some of the other regular totes out there...