If youre travelling at speed then the rope has to absorb a lot more energy when it takes your weight than if you were moving very slowly.
Say you were travelling at virtually zero m/s the kinetic energy the rope had to absorb would be virtually zero, if you were moving at a greater speed the energy the rope has to absorb is much greater
for the purposes of this I have to work in kg so your weight of 193lbs is approximately 90kg
Kinetic energy = 1/2 mv^2
where m = mass in kg and v = velocity in m/s
so if you were loading the rope very slowly your velocity may be 0.05 m/s and the energy the rope had to absorb would be
1/2 * 90 * 0.05^2
= 0.11 Joules of energy the rope has to absorb
If you were to fall 20 ft onto the rope (20ft = approx 6m) the energy the rope would have to apsorb much more energy. To make it easy to calculate I'm going to use a height of 10m to fall onto the rope because if you were to fall 10m on earth the acceleration due to gravity would mean when you hit the 10m mark you would be travelling at approx 10 meters per second (earth gravity accelerates at 9.8 meters per second per second)
now the energy the rope has to absorb after a 10m fall is
1/2 * 90 * 10^2
=1/2 * 90 * 100
=4500 Joules
You can see a relatively small fall puts a huge amount more strain on the rope. Thats why 'full size' climbing gear typically can take an effective weight of something like 22,000 Newtons (over 2000 metric tons) because if a human falls a long way their effective weight on the gear is many many times more than their actual stationary weight
Obviously you should make your own choices as to what you consider safe but if I were in a situation where I may fall onto a rope I wouldnt trust anything less than full thickness climbing rope (ie 10 or 11 mm) If I were rapelling I wouldnt trust anything less than 6mm and preferably at least 8mm unless it were an emergency.