Not normal for most red buds. There are some "weeping" forms, including one called Ruby Falls that looks a lot like yours
but yours clearly hasn't been trimmed in a LONG time. Pruning a weeping tree is not something I have done, so hopefully some one that knows more will come along. But to start with you want to prune off all the stuff that is trailing on the ground. Cut out any dead diseased or broken branches. Cut out branches that are crossing each other and rubbing. Cut out any branches that are growing upwards from the top.
Then you have to decide how much to thin it. That's a personal preference kind of thing. Sometimes people thin them down to very few branches so that the structure of the tree is more visible:
But a lot of the pictures of the Ruby Falls that I saw looked pretty much like yours.