A weeping cherry is supposed to only weep, but this tree has a split personality.
The bottom of the tree is skirted with pendulous branches.
But the top of the tree has no signs of weeping at all. And looking up into the canopy, all you see are branches reaching for the sky.
A weeping cherry is often made by grafting: a non-weeping variety is left to grow until the trunk is about four or five feet tall, at which point the branches are cut off and the weeping cherry is grafted on. The original tree can still throw up branches from below the graft, and if these aren't cut off at the base, they can end up dominating the tree.
That's what has happened here. Both types of branches are different varieties; they might even flower at different times. The only way to make a uniform tree at this point would be to cut off all of the weeping branches.