A better explanation will be along soon, but broadly... In war, the book becomes advisory. An overweight aircraft will take a longer run to lift off and climb, but the crew will be fairly certain that it will. Safely overweight? I believe mil aircraft have published normal operating weights, and military operating weights for when the going gets tough. I seem to recall the c-130 could go 20,000 lbs overweight in extremis- 155,000 up to 175,000.
CG