There are several kinds of drywall anchors and they each have their own weight rating. Some work by drilling a small hole and tapping in a plastic sleeve and others work by drilling a bigger hole and screwing a plastic sleeve and there are others where you drill a hole and the metal butterfly expands behind the drywall know as molly bolts (thanks comments!). Recently I saw anchors where you drill a 1 inch hole in the drywall and this big contraption grips the inside of the drywall (wish I could remember the name). Anyway, each of the big drywall anchors could hold over 50 pounds!
The positive response got me to go dig for those contraptions. Turns out they are made by Moen and they're called SecureMount. I have the Moen SMA3000 and they really are just a bigger version of toggle bolts (spring loaded metal wings that fold and have a long machine screw).
I also found this useful link that has pictures and describes all the types mentioned (except the SecureMount of course . . . those are new and very much a niche product).
It's difficult to model the situation with rational analysis, there's too many intangible factors. You could do an empirical test. You need to support 20 lbs per fastener. We can apply a safety factor of 3 for ultimate strength, so the fastener should support 60 lbs without actually breaking. So you would need 2-4 fasteners to support your weight. Round down to the closest whole number. Install the clips as you did in the wall, except now install a metal strap between the screw head and clip. Arrange the straps so you can step into them to weight the system. Arrange the straps such that your weight is distributed evenly to each fastener.
Weight the system and see if they break. If you live in a seismic area, bounce on them a bit and see if they break. You'll either be able to sleep better or you'll know what to do next, depending on the outcome. Obviously there are better ways to set up an empirical test, I chose to illustrate a quick and dirty method just as an example. Be sure you are protected from flying shards of metal.
Regarding an increaser for the number of fasteners. No, you can't do that. It is a valid concept though, for example you can use a higher allowable bending stress in multiple floor joists than you can in a single use situation such as a header. The concept is not generally applied to fasteners.
Response to OP's Update
Shear strength in relation to fasteners partly depends on what the fastener is holding. In this case it's known as a metal side plate condition, meaning the expected failure mode will either be the top of the screw failing through the shank (shear) or the wood collapsing under the compression from the screw. It's rare in reality to have a perfect shear condition, there is usually some bending and tension components as well.
A true shear condition would something like a metal strap screwed to the wood surface and all the force was parallel to the wood surface, exactly perpendicular to the screw shank. In your test, you mostly have the vertical shear component, but there is a tension component as the center of mass is away from the wall surface. We can safely ignore the tension component in calculating a working load since 80# in pure shear is more conservative than 80# shear and, oh... say 15# tension combined.
A picture of the clip was helpful, I imagined a much worse condition. Either way, the ultimate strength will not be proportional to shear alone, there are other factors difficult to model, thus testing is the best approach. The failure mode you experienced is a bending failure, but your actual installation, while having a bending component, is in fact mostly a shear condition.
The duration of load is a factor. The usual allowable stresses specified in construction are for permanently applied loads. The allowable stresses can be increased for shorter durations, 15% for a few months, 25% for a few weeks, 33% for a few minutes. Meaning we should reduce the allowable load determined through short term tests accordingly. But we also don't know the ultimate load since you didn't achieve failure. Just as well, uncontrolled destructive testing can be a little too exciting. You also haven't run multiple tests (I assume) to confirm you are getting consistent results.
Let's say you did run multiple tests and they all actually failed at 80#. When you apply the 3x safety factor, then adjust for duration of load, you end up with a working load of 20#, exactly what you need. Considering there was no failure experienced, and the installation does appear to be predominantly shear, I think your installation is safe. Barely. Next time around, use heavy ordinary wood screws ;)
Best Answer
Deck screws are unsuitable for that use. They are light in gauge and usually have a bugle style head. You spaced them very close together so you are 'getting away with it' for now.
Most installations don't have a lot of direct pull out pressure, it's often mostly a shear load. Your installation is almost wholly in the pull out category.
In this situation I'd want a screw with flat bottomed head of a decent gauge (10 or 12 at least) and maybe even a washer to further resist pull out. You can increase the spacing but you'd still want at least 8 big screws. You can use a flat spade bit to drill small sockets or recesses to hide the screw head and washer.
There are various deck building framing screws which would be suitable, choose ones with large heads and thick gauges.