You will never have a problem with 7/64", as long as you follow the right hang angle.
Very important that you get the right angle when attaching your suspension. Remember that under 30* you start putting exponential weight onto the suspension. A tight suspension at 90* with 200 lbs down force will generate up to 2,000 lb force on the suspension.
To see what I mean check this out if you haven't already. http://theultimatehang.com/hammock-hang-calculator/