I'd cut it off and be done with it. The loss can't hurt much.
Lightly covered with mulch works also. It needs some anyway.
Mike

Haha, mike, you startled me at first, until I realized you meant cut off the exposed roots. I went back after first post this morning and added mulch so thanks. Just absorbing how to get it to grow vertically as gardengal said. I'm hoping she will come back and explain a bit more. I'd like it to be about 6' minimum. I love the droop, but want the height. I do love trees though. Thanks.

I can't see from the photos clearly where the topmost branch is but that's where you want to start staking it. The branch needs to be pretty flexible - that is, the wood not so stiff that you can gently lift the branch to a more vertical postion. Position a tall stake as close as possible and attach the branch to it so that the branch is pointing upward rather than horizontal and drooping. Once the wood ripens and stiffens in that position, you can continue to affix more of that branch (or others that emerge from that area) until you achieve the height you want.

Much easier to show than to explain but I hope you get the idea :-)

If you click on the first photo, it enlarges and i believe you can just make out the top branch. Thank you, thank you. I understand what you are saying and will proceed to do that gardengal48. I've read some other GW Garden threads on these trees, and may cut off some of the lower branches. I take it this cut is at the widest bud of branch meeting trunk, so that it heals over.

I appreciate all's feedback and encouragement so very much.

Yeah, I meant the exposed roots. I should have been more clear. Duh. :-)
I think of weeping maples as a thin canopy like an umbrella, and prune accordingly. That way, it leaves the edge scalloped.
I prune a little more aggressively than most folks. Here's a picture of one of mine I just took. The upper branch on the left is a strong candidate for removal, but it looks good from the side it's most often looked at. It has been in quite a bit of shade the last few years. Looking south
Mike

It's beautiful in the partial sunlight with those windy branches and wispy leaf fronds. Reminds me of an Ansel Adams photo. Is that the graft at the bifurcation of the trunk? How old is your tree if you know? Thanks for the tips on pruning. Your land is wonderful and I can just imagine the coolness of the NW. Beautiful day there.

Yes, the graft is right where the lichens are growing about a foot up from the ground. I planted it in 1980. That when I planted the Noble Fir, Abies procera, behind it also. That's a Hinoki on the left. I'm surprised at the amount of growth over the years.
Mike

Okay, I went out and staked up the most apical non-wooded branch this morning. I'm thinking about whether to remove lower branches still. I also looked for the graph again. I see one bifurcation above the rings, so that must be it I guess. I can't seem to post multiple photos or even one.

lowest bifurcation of trunk, possible graft site?

Update: Here is a photo of the most apical stem, tethered by light green flex wire to the support pole, in the hopes of promoting a little more vertical tree growth. This stem has 3 branches, all malleable, so I attached all three to the pole vertically. Can't see all 3 well in photo, so trust me.

Last night, I wondered how this vertical growth will integrate with the looks of the bushy growth below. The vertical spot will be above the bushy part: will it eventually bush out too? Oh well, it's a future looks issue; the tree will provide the answer. Patience needed.

Sadly, today I accidentally snapped the still malleable main apical branch back to it's bulb and managed to shear off about half of it from the bulb. All this with a light touch to more vertical: "snap". It wasn't intentional: i realized the way I had fixed to the poll was like 45 degrees, and I was trying more for 80 to 90 degreesl. I now know to leave well enough alone and I'm pretty upset with myself.

I couldn't do the obvious next step, lop off this head branch. I just let it fall back to the stem. It doesn't dangle loosely or hang, but I know there is no "glue" which will magically allow phloem and xylem to nourish this most top branch and 3 stems, and that soon it will be dead.

Since the tree is 4 years old, maybe it's at it's peak height anyways?. I hear these can grow to 7 to 8 feet and that would be perfect for my needs, but you can't force Mother Nature. :(