The strap on my MidwayUSA large range bag did not hold up to the bag's carrying capacity. In my opinion, the MidwayUSA bags are cheap - as in not all that well made and relatively inexpensive (to other, well-made bags).
If you want a bag that will haul more than you can carry, check out Veto Pro Pac. They're not specifically made for the range (they're made for tools) but you cannot beat the quality and features.