Can you post a photo? The layering and crossing branches are just the habit of growth on these plants and seldom requires much attention. Sometimes these are thinned out to open up the crown and reduce the potential from snowload damage but that's less of an issue here than it is where snowfalls are more routine :-)

Generally, my suggestion is to refrain from any pruning unless to enhance or accentuate the natural growth habit.

The crossing/touching branches in Pic 2 are the most concerning. Any thoughts there?

I just listened to a talk from Frank Byles an international authority on Japanese maples. He owned a nursery in Olympia Washington that dealt with mostly Japanese maples, has donated hundred of these plants to local universities and college gardens, such as the UW Washington Park Arboretum. His late father-in-law, Howard Hughes, (not the billionaire) owned a Japanese nursery in Montesano Washington where he sold his plants via a catalog through out the world in the 1950's, even creating several cultivars of it. Frank said pretty much what gardengal48 said. He did say remove all dead branches at the point of origin. Also that second picture he would have said remove all crossing branches that are rubbing, That can cause a point of disease entrance. Now would be a good time to do trimming.

I didn't see any grafting (the technical term inosculated that gardengal48 used means) but then I didn't see any rubbing either. But it is your plant and if you don't like the rats nest look then remove it. Just don't cut more than a third of the living branches away. And if any of the branches are grafted and meet your standards then leave them for the reason gardengal48 says.

None of the branches are grafted. I love the way it looks, especially in leaf. I was concerned with the branches that are touching one another. I have no plans to remove all crossing branches, but am considering the ones that appear to be touching in a way that could cause the bark to become damaged. And I get your point Ggal, these branches are very rigid and it's in a protected spot, it would take tremendous amount of wind bursts to make much movement. It may not be an issue at all. I'll keep an eye on it and see what happens.

Thanks.

Look at photo #2, far lower left hand corner. Is not the upper branch now attached (inosculated) to the lower one? Sure looks like it to me!

And just let me say again that in a weeping laceleaf maple like yours, touching branches are not really an issue.

Ah, I see what you're looking at. The close up in 2 is the upper right in pic 3. What you're pointing out is a branching joint on one of the main trunks.

Posting for contrast now that it has leafed out for the summer.