Wallace - a double float is a flaw in the weaving. That one thread instead of going

Over 2, Under 2, Over 2, Under 2, Over 2, Under 2 goes
Over 2, Under 2, ............Over 4..........., Under 2

So that thread has a float on the top of the fabric that is twice as long as it 'ought' to be. There was an error in the way that the heddles were threaded. You can tell that because the same flaw appears over and over again up the selvege edge. If it had been an error in treadling, the flaw would have been a skip in the twill line across the entire face of the cloth.

But it didn't become a real issue until the prior owner snipped it out in several places; the structural integrity of the cloth was destroyed by that, causing a hole to open up and fray bigger with wear.

When you are inspecting a length of cloth, look for both types of errors, and mark them to work around. For this error, I would have used the opposite selvage for the bottom edge and buried this edge in the waistband (or cut it off). If the error was on BOTH selvages, I would have done a needle weave correction of the flaw at the bottom selvage on both aprons and probably pleated to a stripe that buried the flaw at the back of a pleat. It's actually easier to work around this one than a treadling error that destroys the twill line across the entire width of the cloth.

I really do need to set up my loom with a gamp and do a weaving tutorial, don't I?