Yes it does look like the drapes are too heavy because the hook is pulling sideways I think I would have gotten some extra rings and made 2 separate curtains. If you can get some extra rings and some straight hooks(like the end hooks) you can put them in the flat piece between the pleats. That will take some of the weight off the pleater hooks. See what's available and think outside the box

They are 2 separate panels. I have three windows that I've sewed drapes for. The one in the picture, the window is 92" wide and 2 panels the other windows are also 2 panels and I have the same poking thru the top problem with those also.

You don't have enough structure in the heading to hold the weight. Using that tape alone is okay for lightweight or sheer panels, but not much more. Upholstery fabric along with blackout is pretty heavy, especially with 2 widths.

Can't tell exactly how you made your heading but you should have a double 4" heading at the top. The blackout lining can be turned just once. You can also add a strip of buckram in the heading for extra strength. Then pin your tape on and sew.

You'll probably need a heavy duty machine to sew thru all the layers tho. Don't know what kind of machine you have.

You can also make pleats the traditional way without tape, too.