I never thought about leather getting heavy. Interesting! I like the one in the store quite a bit, although the colors are less fun. Is PUL lighter in weight?
I wouldn't use a bag like this to haul All The Kid Gear--my body can't take that amount of weight in any incarnation of a cross-body bag. I use a plain black diaper backpack for that. It's unstylish, but necessary. Mostly the backpack stays in the stroller/car, and I keep my wallet and a few essentials in another bag that I actually wear on my body.