I don't if you are interested in this, but the state of NC ranks mimosa in the Severe' category for invasive plants. To my knowledge, the newer cultivars are not sterile.

Here is a link that might be useful: NC plant lists

I have two SC mimosas and while they are slightly curved I wouldn't classify them as weeping per se. They are more of a low spreading form. I have pictures on my computer at home that I'll post later.

link to summer chocolate mimosa picture

Here is a link that might be useful: