The answer to this is going to vary by keeper. I have my breeders set up in 10 gallon glass tanks. they are set up in 1.4 ratios. As soon as the babies eyes are all the way open, I immediately pull the babies out of that tank. By this time they are capable of eating and drinking on their own. From what I have seen, usually a mom will naturaly wean around 4 to 5 weeks old... but sometimes the baby will continue to nurse much longer than that, and that means less milk for the tiny babies who really need it.
I pull the babies as soon as their eyes are all the way open because right about that time the mom is about to have another round of babies. If kept in longer then that, it definately gets over crouded, and over crouded is a bad thing! If they feel over crouded, they will cull babies to lessen the population... I believe it also has an impact somehow on the number of babies delivered in the next batch (no scientific data on this one, just personal observation) I also have never lost a baby that I weined at this age..... NEVER!
Some breeders who use larger tanks don't pull the babies at all. ASF's have a good family structure so often times this does work with the older children helping to take care of the babies.
However, the down side to doing this is that once the male babies reach sexual maturity, the adult male will sometimes fight them for breeding rights. The adult male will also get his daughters pregnant, and the younger males will get their moms and sisters pregnant.
I have a few different lines (completely unrelated colonies) and I keep close track of breeders and their age. I want to know who is making who pregnant, so for me the more structured aproach works... compared to the free-for-all that happens with multiple generations kept together.