How to increase payload capacity of plane?
I'm not sure what you mean by 'payload capacity'.  Airplanes have what's termed a 'useful load' which is the maximum combined weight of the passengers, baggage and cargo, and useable fuel.

If you wanted to increase useful load, you would have to make the airframe and all systems aboard the airplane which constitute useful load lighter.  This does have the adverse effect of making the structure weaker, lighter engines generally are less powerful so you have less thrust, and removal of mission systems reduces aircraft capability.  Manufacturers strive to address these things and improve them over time with more rigid aluminum alloys or composites for increased strength to weight ratio, higher thrust to weight ratio engines with better fuel efficiency and lighter mission systems.

How an increase in weight affects aircraft performance not only depends on how heavy the airplane is but where the center of ends up being located.  On a conventional airplane a forward CG produces better stability but requires more lift from the wings, resulting in decreased performance.  An airplane with a more aft CG offers better performance, but is more unstable, particularly during high alpha operations such as slow flight.   The maximum takeoff weight of the airplane was established during preliminary design studies and verified during flight testing so that it cannot exceed the load limits of the airframe and offer the required performance over a wide range of potential operating conditions.

Aircraft are, on occasion, approved via a Supplemental Type Certificate (STC), to increase their useful load, if the OEM or third party vendor can demonstrate that the mod can still operate safely and fulfill the regulatory requirements.

At any rate, the heavier the airplane is, the more lift it needs to fly, which means more drag, which means more thrust, which means greater fuel burn.  This is why the airlines are so miserly in issuing out the bare minimum gas to meet federal Part 121 and company SOP requirements for their flights.  The fuel saved doing this saves the company millions of dollars annually.