Trina,
Those are suckers from the rootstock the weeping crab is grafted onto.
You can probably dig/pull them up - and they've probably got the beginnings of a root system; I do this with my apples, and use the rootstock suckers - after lining them out in nursery rows for a year - as rootstocks for new grafts.
But, these are not going to grow up to be weepers - at best, they're a seedling crabapple, but may be one of the clonal rootstocks selected for one or more characteristics, like dwafing, disease resistance, etc.

So, the only way to be sure that I can have a weeper is to root a cutting? Are all of the weepers/pussywillows, cherry, mulberry, etc grafted onto a different rootstock? Trina

Yes. All those you've listed are grafted, either on a 'standard' - an erect stem of variable height - or they're grafted low and staked up to the height you want them to weep from; otherwise, they'd run along the ground like a vine.
Weeping willow(Salix babylonica) is the only 'weeping' tree I'm aware of that is commonly propagated from cuttings and does not require staking.

It's almost a certainty that your weeping crab was grafted/budded onto a seedling crab or clonal apple rootstock, many of which are notorious for suckering from the roots. If you wanted to pull some of those basal suckers this winter, line them out in a nursery bed, grow them up for a couple of years, and then graft or bud onto them from your weeping crab, you could 'build' new ones. Apples aren't particularly easy to root from cuttings; if you managed to root cuttings of your weeping selection, you'd have to stake it up to whatever height you'd like it to weep from.

Thank you so much for the info. I will give it a try! Trina