During the early design stages, what parameters are considered in determining the weight of an aircraft?
Any design starts with a mission profile. As a design engineer, you get the payload, range and speed, and maybe constraints like the maximum runway, and then have to come up with a configuration.

With that in hand, you look what others have achieved before. There are collections of weight data for different designs and their parts, and formulas which combine the main parameters in a way that the weights line up more or less nicely when plotted over the result of this equation. Plug in your new design's number, and you get something wich will be within ±10% of what is realistic. This is called parametric weight estimation (PDF!).

Since you can only consider what you have, you start with the boundaries of the sizing mission:


Payload
Range or endurance
Desired cruise speed and altitude
Operational constraints like runway length, operation from unprepared fields, threat scenario.




EDIT:

@Peter is right: Cost per kilo of airframe and per seat-mile (where applicable) is also a starting requirement, and cost minimization is taken care of by designing the smallest possible airframe which can satisfy all requirements while using proven technology. And parametric sizing only works when based on proven technology.