The take-off weight (mass) available for any given take-off can be limted by a number of things, and the initial question refers to one of those.
Non-scientifically, and from memory here are some;
- Structural and design limits
- Obstacles in the take off path (which widens out from the runway end) which must be cleared by a stated vertical separation, with one engine inoperative
- Air temperature (WAT limits?)
- Need to stop within the available emergency distance after an RTO at V1 ("accelerate/stop"), with asymetric reverse thrust or none at all.
- Need to arrive at the other end with the weight below maximum landing weight
- Possibly on route obstacles (?)
- Others?
The maximum weight/mass allowable under ALL the limitations must be calculated for the airfield and runway in use, route, destination and alternate for the flight, using the official met data. The lowest resulting figure is then used to decide the maximum load of passengers and fuel available after taking the weight of the aircraft, catering and crew into account (APS weight).
Mostly, fuel is non-negotiable (ever tried defuelling?) so the decision bears only on the passenger and cargo weight allowed.
I think that's about it, but perhaps a pilot or dispatcher can put it better and be more up to date.
I'm sure someone will say that we use mass these days, not weight. So please read one for the other because they're right.