I did the same doubling up of fabric on my end channels of my 1.1 oz hammock. I only did three straight line stitches. I have not had it long but it has survived me and my boys hanging in it. Even bounced on it a bit with two of my boys in it with me to stress test it and it shows absolutely NO signs of coming loose.
Most of the stress will come on the ends of the channels so just be sure you have some good back stitching to lock it all in place. I have no doubt you will be fine.