Cherry from seed isn't likely to come as true. One of the most common weepers would be Prunus x 'Snofozam', or snow fountain weeping cherry. I've started many seedlings from this tree & none demonstrate a weeping habit, so that's something to keep in mind. Yes, you CAN bend the tree to a weeping habit, but fighting the trees natural tendencies isn't usually the best course. Letting the tree tell you what it wants to be is one of the ways we work WITH the tree, instead of against it.

If you want clones of a weeper, you might try directing your energies toward rooting cuttings.

It sounds like somewhere you read that pruning the buds off the understock is mandatory if you don't want the understock to out-compete the scion and spoil the appearance of your tree, but that wouldn't apply to a seedling - only to a grafted tree, and then to only the portion of the tree below the graft union.

Al

were you using a dwarfing rootstock?