Sorry Hirashin, I mucked up explanation. Apologies for the confusion. Anyway, I'm trying to find a simple explanation to the reason why c) is invalid:
(c) How much weight is the airplane?
It's wrong for almost the same reason that (b) sounds funny. It has to do with the use of the abstract noun.
How + adjective + is the airplane? (heavy, full, fast, big, etc...) Is a normal, correct construction.
How much + abstract noun + does the airplane have? (power, energy) Is also a normal construction
We don't normally say "How much weight does the airplane have?", but it is a valid construction, albeit very unusual. Normally we say "How heavy is the airplane?".
Similarly, we don't normally say "How much height does the airplane have?", but it is a valid construction. Normally we say "How tall is the airplane?".
But we would never say "How much weight is the airplane?" because the abstract noun clashes with the How much and the verb is in that construction. As above, you would need to change it to: "How much weight does the airplane have?", because weight is a quality that the airplane has, and not a quality that the airplane is.
I hope this is a more satisfying answer. My previous one was very sloppy.