What weight did you guys find acceptable for your robot for it to reliably not burn out during competition for these gearings? I’ve been having some issues
4 motor 1:1.6 (direct drive and non-direct drive)
6 motor 1:1.6 (direct drive)
6 motor 1:2
All three of those configurations work. I’ve had all three of those this season. Try to keep your robot under, say, 15 lb, but weight is generally not the issue with stalling. If your drive stalls, check your breakers, look for shorts, and ESPECIALLY test for friction.
My robot is a six motor 1:2 drive and weighs 18 lbs. It will only burn out if I try to push or fight with another robot. Any of the drives you posted should work, if they’re burning out it’s probably because of excess friction.
Something that can make a very big difference is if you chain/gear the motors and wheels together. This way you always have the combined force of 2 or 3 motors to overcome before a stall. If they are separately attached to each wheel, it is possible that one of them can stall (less strain needed to stall just one by itself), and then the other(s) have to drag that wheel along, making it likely they will stall afterwards.
Hopefully that makes sense.
Should I be worried if my robot weighs almost exactly 15 lbs as a 4 motor direct drive?
Not at all.
You should be fine off with 4 motor drive geared to 1:1:6 but if you want to be more safe 6 motor drive geared to 1:1:6 or just gear for torque and it will fix the issue of stalling if you’re worried! Make sure your robot does not weigh over 15lbs. Check for resistance and friction if its stalling, also check the motor controllers and wiring to make sure everything is working. I have tried 160rpm and had some stalling problems but that’s just due to driving for a long period of time! 
Our robot uses 6 High Speed (1.6:1) motors. Our robot is 16.125 lbs, with fully charged batteries in the robot. We have not had any problems with our base stalling. We are using indirect chain drive of all 6 motors. I say if your robot is light you can use 4 motors, other wise use 6 (on high speed) to be on the safe side.
So if a bot were to weigh 18 pounds… is there a ratio that is good to use between the 1.6:1 and 1:1? (4 motor drive)
Holy cow! I would just use 1:1. That’s REALLY heavy. 1:1 would be your best bet, as I am quite sure 1:1.6 would stall pretty fast.
It should be fine. I have a 25+ pound robot with a 4 motor drive at 1.6:1 that can drive around the field without browning out. It’s slow, yeah, but completely stable. You just can’t get into a shoving match.
EDIT: I should clarify. That does NOT cross the bump. This is on just the flat part of the field.
Haha okay. But I mean seriously, if I go and try to push you and you fight back, your motors are going to die extremely fast.
Basically instantaneously. It barely pushes buckyballs.
Does a dead battery weigh less? 
Sorry, I just had to…
Well, 3000 mAh at 7.2 V is 21.6 watt hrs or 77800 J. 77800J/(3000m/s)^2=8.65x10^-13kg or 1.91x10^-12 lbs.
Sorry, I just had to…
I don’t know I just wanted to measure the robot in prime condition.
Ummm. You might want to look into that.
Ya, our drive wasn’t as bad as that, but the thermals in the drive motors still cost us many matches of not moving. I do admit that I am not the best driver, and our other driver was very rough, but it still was quite a design flaw.
Electrons have mass, so it is possible that a charged battery weighs infinitesimally more than a dead one.