The weeping part of the tree is grafted onto what the trade calls a standard. The standard is another tree, different than the part grafted at the top (weeping cherry in this case). The standard is usually the same species or a relative that is compatible with the grafted stock.
I don't think you have a reversion. I think it is growth from the non-weeping standard. I'll bet that if you follow those straight branches to their origins, you will find they begin below the graft union where the weeping part of the tree begins. I have never heard of weeping cherry reversions, but I am sure it is in the realm of possibilities.
If this is the case, snip the straight branches off at their origins. Make as clean of a cut as possible. Rough and ratty cuts can encourage more sprouting from the same wound.
