For a commercial operation, the aircraft dispatcher. For a private pilot flying on their own, the pilot is responsible. Charter operations vary, its the pilots responsibility but some choose to hire flight planners and/or dispatchers as well and the responsibility is delegated to them.

The numbers and charts are found in the airplane manual for small aircraft, for commercial jets a separate manual is generally produced for the performance charts; my airline calls it the Operations Data Manual, or ODM. Our engineering team has gone through the ODM and coded all of the numbers into our flight planning system, so that as we plan the flight and update items like passenger count and the weights for checked bags and cargo, the system automatically updates and displays the numbers for those conditions for us to cross check and verify.