Most of these multi speed mini velos seem to come in around 25 lbs. I recall someone saying that was the weight of their BD mini velo, and that's about what my Cannondale Hooligan 3 weighed in at. I'm willing to think that the Big Shot is probably somewhat lighter, although it hasn't got all the same components as these other bikes at all.
They could certainly go a lot lighter. Of course, none of these bikes are extremely expensive either. I think the Big Shot, Hooligan 8 and BD mini velos all come in under $600. They're a pretty decent weight for the price.
One of those Big Shots with a little front porteur rack and a 3 speed gear hub could be a lot of fun to me