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.

Thanks,
Jim