Help! Sewing with Home Dec Weight Fabrics

Hello.  I have sewn many things with Home Dec weight fabric.  But this is the second time I have had the same problem.  The first time I was using Sunbrella Fabric and noticed when I pinned the two pieces together to sew and ran it through my machine that the top fabric started sliding or moving, then you end up with it either sewn folded over in a spot or the the top fabric has moved out of line with the bottom fabric.  I am using a heavy duty needle (110/18) and a foot that came with my machine that has a metal roller that I thought would help feed the top fabric.  This seems to help most of the time, but when I am sewing 4 layers, the top fabric again starts moving. 

Does anyone have an idea of what to do or what I am doing wrong?  It is driving me crazy and I am sewing 20 Chair pockets for my son's class and I have only gotten 3 done so far and I am not looking forward to the rest. Any help is appreciated!!!!

Try using a waking foot, it is also called and even feed foot.  If one did not come with your machine they are fairly generic, you need to know if your machine has a short, long, or slant shank when you buy one. 

If your machine has a setting to adjust the pressure foot pressure I might try that too.