The basic physics of the question is fairly straightforward. The amount of power it takes to lift an airplane off the ground and keep it in the air increases with the weight of the airplane. There is a maximum amount of weight that any given airplane can carry safely.
Given that there is a fixed amount of weight an airplane can carry, airlines need to make choices about how to allocate that weight. The actual decisions of airlines to reduce the amount and weight of luggage passengers can carry is based as much on the profit motive as on physics.
There are three basic ways an airline can increase revenue for a flight. The first is to charge more per seat. This strategy though is vulnerable to competition, because if an airline raises prices, passengers will choose other, cheaper airlines.
The second way to increase revenue is filling a given airplane with more passengers, by reducing seat size and the space between seats. When airlines do this, though, they run up against the laws of physics, in the form of the maximum amount of weight that an airplane can carry safely. Thus, to compensate for the increased number of passengers in planes, airlines restrict the weight of luggage each passenger can carry.
Finally, airplanes increase profits by limiting the amount of luggage a passenger can carry for free, and add surcharges for "excess" baggage. This is simply a way of charging more for the same service, but in a manner that won't show up when passengers initially purchase a ticket, making the cost of a flight appear less than many passengers will actually end up paying.