Hi Vincent,
The growth you see going straight up is from the root stock the weeping stock is grafted to. This is undesirable growth and needs to be pruned out; it will never 'weep'. Often the root stock is the stronger of the two in a grafted tree and if not kept in check will take over.Fall is not a good time to prune trees or shrubs because it can stimulate new growth that doesn't have time to harden off before winter sets in. The new growth is too tender and can easily suffer 'winter kill'. Late winter pruning when the tree is dormant is the preferred time.
Prune out any branches not weeping at the trunk where they originate being careful to leave a 'collar'. The collar is a swollen area near the trunk and it will sometimes look wrinklely. Leaving a collar will help the tree heal quicker. But don't leave stubs sticking out either.
If you need a diagram to follow check out some tree care books at the library. Pruning can be enjoyable once you have some background in the correct procedures.
Bye, Diane