The twig stuck in the pot on the left is a cutting from another tree. You can barely make out the new shoot rising up in the center to the left of the stake. There's just one leaf on it. I circled it in red.

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The weeping forms of JM's don't really have leaders :-) Many times they ARE staked to increase vertical growth before allowing them to develop their natural, spreading, weeping habit. It is a personal choice to do so or not. I tend to remove any stakes as soon as I purchase them, as I want to encourage the umbrella shaped form over height.

To be honest, I most likely would have selected a different specimen initially, as the growth on the one in the photo is not at all what I'd be looking for in that cultivar.

I realize the form on this tree is less-than-optimal. That's why I was able to get it for $8. Actually, it was better than the other available choices. (You can tell it didn't get sun either by the green coloration.) I bought a #2 Tamukeyama that is almost perfect form, but I picked this guy up while I was at it b/c I've always like Red Dragon.

Be that as it may, I am not one to give up so easily on a baby tree. A lot of things can happen as a plant matures. I also prefer the more umbrella-shaped trees and I expect that at some point the leader will bend over and weep. My question is:

Should I stake one of the two branches this tree has or should I wait to see what becomes of the new growth I circled?

If it was my tree I would try and stake the largest branch upright, assuming it is flexible enough. You could also pinch out the tips of any vigorous shoots on the ends of the other branch to discourage growth here.

Give it a couple of years and you might have a tree with a nice form, bargain for $8!

Thanks for the response. Both branches are still flexible enough to be staked. I will choose one (probably the one on the left) and stake it so that the tree can gain some more height. Hopefully, another branch will develop horizontally.

Dimi
Sometimes a ugly duckling turns into a swan!!
I have about 10 JM's and some have 2 trunks and I am a cutter so I just keep working with them and I think they are all beautiful.Also I have fruit and other trees that have 2 or 3 trunks IE olive and pomegranate I try to make all my trees in ground bonsai

good luck

Update here:

I did stake one of the branches to form a leader. It looked funny at first with all of the leaves turned sideways, but the tree is now adjusting and the leaves almost look natural. I guess trees are smart! The coloration is turning much more red now, too. It has no tendency to weep, but I don't really want it to do so at such a short height anyway.
I'll post another picture as the season progresses. Thanks for the encouragement!

Many weeping laceleaf Japanese maples grow as low mounds for decades, if not trained to have some height. I've had one for over 40 years that is still, I think below chest level - it has no structural interest except when leafless. Ones trained into a tall, conical shape can look a bit odd but when these dwarf trees are not trained up at all most of their potential may be lost. The point of weeping trees is their cascading or drooping branches, the main framework needs to be elevated enough to allow for this.

Or overhanging a wall.