Lolwut....
Huh, I just realized how those buttons never really do anything...
Anyways, you don't add backgrounds that way, you simply place the new files in the Data/Stage folder and they'll show up when CE reloads.
It's important to note that each background needs two things:
The .PBM, usually called PrtXXXX.PBM, where XXXX is the name, say Pens or Egg.
And the .PXA, which should be named somewhat similar. {I just realized I named my wrong. The original ones have the same name as the Prt's, but without the Prt. Leaving them on doesn't seem to be bad, though}
The .PXA is where the game finds out what each tile actually does; is it a slope, solid ground, water or just empty space?
I recommend coping an existing set and then editing the .PBM with whatever you want.
Edit the .PXA with CE, though.
EDIT:
Wow, what did I just do?
That's for tilesets....
*facepalm*
Well, if anyone had any questions over those...
Anways...!
Backgrounds are simple.
In the Data folder there are bkXXXX.PBMs, with X being the names.
Simply copy one or make a new .PBM there with bk as it's starting name, but keep the dimensions as multiples of 16.
{16x16 would work, so would 32x32, 16x32, etc. The dimensions might not matter, but the 16 multiples match the standard block size of Cave Story, and would make it look very clean and nice. But, meh, I haven't played with backgrounds yet}
If you want something special like the moving backgrounds for Balcony and Outer Wall, I'm not entirely sure on how those work, but I'm guessing the pixels it moves are set in the EXE, so you'd have to copy the original and modify it, marking the location of the tops and bottoms of cloud layers and such.