Will a 6.1 oz. cotton bag weigh 6.1 ounces?
Not likely. Here's the tricky thing about fabric weight: when people discuss it in terms of ounces, they're speaking a form of shorthand. We're going to break it down for you, right here!
Let's take that bag made from 6.1 oz. cotton. The manufacturer isn't referring to the weight of the entire bag, but rather how much a given amount of the cotton weighs. When manufacturers calculate fabric weight, they take a standard-sized piece of the material (often a square yard) and weigh that on a scale. A square yard of the cotton from the bag would weigh 6.1 ounces.
The proper unit for measuring fabric weight in this case isn't an ounce, but an ounce per square yard (oz/yd2). So why does it get shortened to ounce? Convenience, most likely. Or to give you another reason to go looking for answers on the marvelous Quality Logo Products website!