Assume your average weight is wrong by 10 pounds. You have 300 people = 3,000 excess pounds. A 777 has a OEW of about 310,000 lbs, so you're off by, at most, 0.9%. (At MTOW, you'd be wrong by 0.5%)
If your large airplane has a 1% margin between safe takeoff and a crash, then I'd say you have a severe design problem. It's really a problem in very small aircraft, like the BE1900, not in anything mainline.