Without knowing anything about the specific aircraft or airport, some general reasons that you might be weight limited would be:
1. Runway length - short runway requires lower weight to allow the aircraft to take-off OR abort the take-off safely.
2. Obstacles surrounding the airfield - mountains, buildings, and towers may dictate a lower aircraft weight to allow it to climb sufficiently after having some kind of engine failure.
3. Hot day - heat reduces aircraft performance which affects it's ability to take-off and climb.
4. Airport at a high altitude - Like heat, the lower atmospheric pressure at high altitudes results in a loss in aircraft performance.
5. Fuel requirements - A long flight on one day may require less fuel than a short flight on another day as extra fuel is required if the weather at the destination is forecast to be dodgy.
Each of these factors may have a minimal impact on their own but sometimes you may be affected by several of them.