Would you still fly if your weight was over by 20 pounds? I know there's maximum gross weight and a maximum take off weight. In all reality, how far over is too much. I can understand 200 pounds overweight but 20 pounds? Hell I'd burn that off before top of climb.
It's not so much how many pounds you're over, but what percentage. I'm going to address everything mainly at the bottom, but the first thing:
20 pounds overweight is the gateway drug.
This. If it's OK to go 20 pounds over, why not 30 next time? If 30 works, how about 45? How about 75? This is normalization of deviance. It will kill you eventually, you just don't know when. Don't want to die? Don't even start unless you really know what you're doing and jump through the appropriate hoops to do it legally and safely.
Over weight better than out of CG?
Honest question.
Depends on whether the trees at the other end of the runway are FAA standard 50 footers or if they dared grow higher. Or if they're shaped like hills, or it's a hot day...
Generally speaking, provided you still have enough performance to get off the ground and not hit things, then yes it's better to be overweight and within CG than to be out of CG. One of them hurts performance, the other hurts controllability. I'd rather have crappy performance and be in control than vice versa.
... which is only good for 121 and 135 in Alaska, and those operators will have FAA approved procedures in place to ensure that the safety issues presented by operating over max gross are mitigated.
Now, on to the real answer, or at least, what you need to consider before you decide not to do this (hint):
1) What is the reason for the MGTOW being what it is? Is it structural, aerodynamic, certification, etc that is the limiting factor? For example, the 172N and the 172P are structurally the same, but the N's MGTOW is 2350lb while the P's is 2450lb IIRC. The difference is that the P model only allows flaps to be extended to 30 degrees instead of the N's 40. One of the certification requirements for part 23 is the ability to do a go-around with full flaps, and the 160hp 172 could only do that at 2350lb and 40 degrees of flaps, but could do it 100lb heavier with only 30 degrees of flaps. So if you're flying a 172N, can you probably safely fly a little over gross? Probably, IF you don't have to go around with full flaps.
2) Do you still have the performance necessary to complete the mission? Runway and climb performance is generally the tough part here, but depending on how far overweight you go there may be other factors at play... And of course your performance charts are only good for up to MGTOW. Famously, Piper test and delivery pilot Max Conrad flew a Comanche 250 nonstop from Casablanca, Morocco to Los Angeles in 1961. He was WAY overloaded, the aircraft had a MGTOW of 2800 pounds and he was loaded to 4800 with all of the extra fuel needed for that record-setting trip. He also needed nearly the entire 8,000 feet of runway just to become airborne and he barely cleared the fence.
3) Do you know how to calculate performance and V-speeds at weights above MGTOW so that you can extract the necessary performance from the plane? Linear extrapolation doesn't work - Climb performance, for example, is related to excess horsepower and you need at least a couple of good reference points in similar conditions to make this calculation. Some V-speeds stay the same, some will change, mostly with the square root of the ratio of the weights.
4) Will your W&B still be in balance even above gross? Most CG envelopes get narrower as you get heavier, so if you go too far over gross you'll be out of the CG envelope, period.