I definitely agree with weeding more frequently.
Think of a root system as a battery, and the sun as the charger. A seed is a fully charged battery and, as the tree grows, it's continuously being "charged" by the sunlight, with the excess energy being stored in the root system (the goal is to grow quickly while still storing
enough energy to make it through the dormant season).
When you weed and break the stem, the tree is no longer getting charged by the sun via photosynthesis, so it relies on the stored power in the roots/battery to push new growth. Once the leaves are hit by the sunlight, it begins using that energy to continue growing while storing any excess in the
roots to make up for what was used to re-grow from the broken stem.
What you want to do is, essentially, drain the root/battery of the stored energy. This is accomplished by pulling/breaking the stem, again, before it has a chance to produce enough leaves to fully recharge the root system. Eventually, the "battery" will run out of power and shut down, causing the plant to die.
When I weed oak & elm seedlings every spring, I've found it works best if I go through, at least, once a week and clear the area. This allows me to get any new things that have sprouted since the last time, find the ones I previously missed, as well as pull/clip the ones that re-sprouted due to broken stems. It seems that after the second attempt to grow is usually enough to drain the stored energy and keep it from trying it for a third time. If I wait more than 2 weeks, or it's a bigger seedling, it seems to allow them to store enough energy to go through more cycles of regrowth. A smaller battery may charge faster, but it doesn't store as much power; while a larger battery takes longer to charge, but can store more energy.
Of
course it varies depending on the type of tree. Rhizomes *may* have more energy stored & require more chops to drain it. Crepe myrtles & chinaberries are small seeds that quickly build a bigger root system to store more energy, yet a pecan has a bigger seed/battery, but spends time/energy on a big taproot while depending on the stored energy before putting out a lot of feeder roots. Regardless, the principle is the same- drain the stored energy before it has a chance to power up again.