There is a lot that goes into determining the maximum takeoff weight for a aircraft. To keep it simple there are 3 numbers. Max structural weight limit, runway weight limit and climb performance weight limit. Leaving EIS the critical number will almost certainly be the runway limit because of the very short runway.
That limit is based on the maximum weight the aircraft can accelerate to and either reject the takeoff or continue and get safely airborne with a engine failure. If the runway is wet it requires more stopping distance if the takeoff is rejected. On a 4600 foot runway you would have to reduce the takeoff weight substantially to be legal.