Weiss wouldn't stand a chance, the Deepground members are just another one of Hojo's experiments to try to create another Sephiroth.
Whoa, there cowboy, you're way off base on Weiss and the Tsviets. Hojo, who had a major hand in Sephiroth's creation, made Vincent, has fought Cloud, and seen many insane creatures says in Dirge of Cerberus "Then I remembered Deepground, home to the most powerful beings on the planet."
Now at this point Sephiroth is gone, so he isn't in the equation, but this means Hojo, who knows the strength of every great warrior on the planet, considers the Tsviets to be above Cloud, Vincent, the rest of Crisis AVALANCHE, Genesis, and everything else. When you consider that Weiss in his base form completely owned the shit out of Rosso and Azul in their strongest forms while he was only using one hand, and taunting them the whole fight, base Weiss is about equal to pre Nibelheim Sephiroth. Omega Weiss, while not equal with AC Sephiroth, is around his level and there is a good chance that he could beat him.
Here's a link to the video of base Weiss in action.