Need some help with a young Mimosa tree

I have a Mimosa tree that is about 4 years old. It grew from a seed in my flower bed and I moved it to the middle of the back yard a couple of years ago. Over the winter, with no leaves on it, it was just a stick about 2 feet tall. It is now about 7 1/2 feet tall. While that may sound like it is a very healthy plant, it isn’t branching. The entire trunk is growing like it was a limb. It just produces leaves as it grows. Also, it can’t hold itself up. If I disconnect it from the stake it is tied to, it droops all the way to the ground.

So, what should I do with it. Cut the end of the limb/branch/trunk to force it to branch? Strip the leaves away? Just leave it alone, tied to the stake and it’ll take care of itself?

Any help would be appreciated.