What parameters are considered in estimating the weight of an aircraft in the beginning of the design process?
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:
- Range or endurance
- Desired cruise speed and altitude
- Operational constraints like runway length, operation from unprepared fields, threat scenario.
@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.
When designing, the designers have to take into account:
The amount and type of materials used on the airframe. Many aircraft made nowadays use composite materials because they are stronger and lighter than metals. The engines also play a significant role in this because they have to create a certain amount of thrust without adding too much weight.
They also have to take into account the payload that (amount of fuel, passengers, and/or cargo or other things) that the aircraft will carry.