A couple of things...the weeping part is grafted to the top of a regular Redbud. The remainder will sprout new leaves but it will be a regular Redbud (no weeping).

The bit that broke off is too big to root as is. It would need to be in much smaller pieces to even have a chance. Redbud is also not easy to root from cuttings (technique & timing are critical and still success is mediocre) and the resulting plants are reported to be of inferior quality and poor growers.

If you are still craving a weeping Redbud, you should buy another. If a Redbud tree is ok with you, keep the 3' stub...it will grow into a tree.

It has not been established that the entire grafted portion of the tree broke off, so I think Smivies' advice to start anew is premature. If you can't tell where the tree was grafted, post a photo and maybe we can figure it out, or just wait and see if any new growth continues the weeping habit. The damage will probably not kill the tree.

How could I tell if where the grafted part is? Could the graft have weakened it?

Here are some photos. The bottom looks like it might be where it was grafted. If that's the case, do you think it will grow taller as a weeping redbud? Can I root the part that snapped off?

Oh...one of those weeping Redbuds. Not the ones I typically see that is a standard with the weeping part grafted to the top. Yours looks like a low grafted that was staked upright. If left as is, it will likely be a mounding tree not much taller than it currently is. To increase height, take a new pliable shoot and stake it upright until it hardens off....that will be the new top of your tree. You can keep doing that over a few years until a desired height is achieved...reasonably, you can gain 12-18"/yr that way.

The bit that broke off won't root for you.

I'm afraid the "take a new pliable shoot and stake it upright until it hardens off" is beyond my understand. Is a new pliable shoot a branch?

The new growth is floppy...that's why it weeps on that variety. Later in the summer, the floppy new growth becomes woody and rigid. If you direct the floppy new growth vertically, it will stay that way when it becomes woody.

If the specimen gradually mounding up on its own seems adequate you don't have to do any training from this point. The value in staking and training small specimens of weeping variants of this growth type is to get a more elevated and pointed crown, from which the weeping branches can hang. Otherwise one might end up with a comparatively low, blunt and broad shape, even after many years. With this being considered less decorative and impressive than a taller form.

The good news is that your tree is still a weeping redbud. The bad news is that it's planted too deep. You may want to replant it or at least try to uncover the root flare, which is the point where the roots branch out horizontally from the trunk. If you don't, you may end up with roots like the ones on my first attempt at tree planting, coincidentally also a redbud. You can see the huge circling root that will most likely break my tree in half if I don't cut it in the picture below.

As to the problem at hand, see if either of those two branches on top can be bent upward. If not, you will have to wait for some new branches to grow to make your tree grow higher, or you could also consider staking up a lower branch to become the new trunk leader. It would probably be best to tie the new leader to a long stick(bamboo is preferred) stuck in the ground. Don't use anything that will cut into the wood like string or wire to tie it.

Thanks, I now get the 'floppy new growth' and I've got one of the top newish branches that will do that.

How can you tell it is planted too deep? I have very little experience with planting but it's counter-intuitive to me to have the roots so close to the surface.

Thanks all!

How can you tell

Taper of stem where it enters soil.

Another school of thought is that when planting a grafted specimen where the use of the stock does not confer any direct advantage to the end consumer such as soil pest resistance or dwarfing of the scion (commonly done with orchard fruit trees for instance) - but was instead simply a convenience for the production operation - it is desirable to gradually over a period of years add soil until the graft union becomes buried.

In the hope that the scion responds to this soil contact and makes its own replacement root system above the graft line, eventually leaves the probably quite deformed stock behind. (In addition to root-bound woody plants being prevalent in commerce to begin with there seems to be an idea present to at least some extent among commercial growers that plants earmarked for use as stocks are even less in need of being kept potted on in a timely manner than otherwise).