I'll make you an example with C172R (as I believe this is the most basic way I can explain it). C172 has a empty weight of 1639lbs and a max take off weight is 2457lbs, that means your useful load is 818lbs. Now it can carry 56 gallons of fuel and has room for 4 people + cargo. Each gallon of 100LL weighs 6lb, 56x6=336. Lets take an average person weight of 170lb, 170x4=680. 680+336=1016, so 100% fuel + 4 people (it has 4 seats) weighs 1016lbs. So again the empty weight is 1639lbs, 1639+1016=2655lbs. Therefore we have an aircraft that can fit 2655lbs (of fuel and people) when the max take off weight is 2457lbs, your 198lb overweight. Keep in mind we did not add any cargo, and there is still room for it.
So my point is that even if you have room for fuel, people, cargo, or ord does not mean your aircraft can lift it. Gyrene, can you tell me if you understand or do not understand, and agree or disagree with my last sentence?
BTW I do not fly this aircraft so my number may be a little off, but if you really want I have the POH and can confirm them.