Invisible zippers come in 3 weights: #2, #4 & #6
#2 are the standard that you find in fabric stores. (2mm across the coil)
#4 or 4mm across the closed coil, are a little heavier & stronger. Use in bride's maid dresses, pillows.
#6 or 6mm across the coil, are the size that Vera Wang uses in her gowns & I use in cushions or slipcovers.
To make your selection of the correct size invisible for your project a little harder, some manufacturers call these #3 & #5 invisible, instead of #4 & #6. My coil is a bit heavier but will normally fit #3 and #5 invisible pulls.
The little plastic invisible foot that you have will NOT work with the #4. Being cheap, I just use my standard zipper foot & stitch in the ditch. If you have a commercial machine, I stock Sam Sloan's adjustable foot in "Thread & Workroom Supplies".
I only stock a few lengths in #4 invisible closed bottom or finished zippers because yardage is so much easier. So if the color you are looking for is not stocked in the length you need, consider yardage. You may purchase with the pulls on the tape or with pulls that you can put on.