No you would not glue the material to the weather strip rails, it is glued the the strips mounted inside of those rails. Mounted to the roof rail inner structure there are headliner retaining strips, mounted just inside the roof rail weather strip retainers. One mounts along the top of the door window and quarter window opening. (see yellow in pic below) The second is short and runs vertically (see red in pic below) from the first strip down along the back edge of the side window opening, the third runs horizontal from the top of the side window opening to the top of the rear window opening. The headliner gets glued (3M trim adhesive) to the first metal strip that frames the top of the side window opening. the third strip that runs from the side window opening to the rear window opening (see blue in pic below) has triangular "teeth" that grab the headliner material. the headliner material then gets glued to the top of the windshield and rear window openings. After the headliner is stretched and glued, the rear sail panels should have extra cloth hanging over the edges,. The extra fabric on the front is glued to the vertical strip (red) at the rear of the side window opening and the upper fabric is glued to the pinch weld at the sides of the rear window opening.
I just installed my headliner a few weeks ago. (more pics in my build thread) I had the luxury of doing it before I installed the windshield and rear glass which makes it much easier. The headliner is glued to the wind shield and the rear glass mounting pinch welds. The headliner is covered by the rear glass weather strip, working as a trim molding of sorts. I would recommend trial fitting the bows and numbering them. They are all different lengths and this way you know you are placing them in the headliner in the proper order.
I have installed quite a few headliners before over the years just for my own cars and friend's cars This time I thought I would get lazy and have this one done professionally. Trim shops in my area wanted $450 in just labor to install a headliner, so I chose to do it myself. It isn't really difficult just tedious, the key is to center the headliner and work out from the center stretching and clipping it down as you go. I buy the extra large paper clips and use them to pre-fit the headliner and to hold the fabric while the glue cures. I like to stretch out the headliner without glue first, using only clips and adjust as needed to get the wrinkles out. After I am satisfied with the over all fit, I trim the excess cloth around the edges to make it easier to work with. Once that is done, I start to glue one small area at a time. I remove 3 or 4 clips at a time and apply the glue and then re-stretch and clip that section before moving to the next.
I'm sorry I did not take any pics of the headliner retaining strips installed before I installed the headliner. I removed them to paint the inside of the shell and did not take any pictures of them reinstalled before I started headliner install. I did take a picture of my inner roof after I painted it and marked up where the retaining strips should be mounted. the first strip location is yellow, the vertical strip location is red and the third strip location that has the "teeth" that grab the headliner is blue.
I would also recommend unfolding the new headliner material and laying it out on the clean roof for a few days. If it is warm enough in the garage the folds will start to work themselves out. You can also use a heat gun or a blower dryer to smoothen out the folds before you install, I like to use a steamer which works better if you have access to one.
Hopefully this helps explain the process a bit. Headliners are not hard they just take patience and time to work out the wrinkles. I am confident you can install your headliner yourself, just take your time and it will turn out great and you can save yourself some cash.
