To get an idea on the weight - I'll make a wild assumption and say we scale the optical formula. This doesn't really work in practice... whatever
Say you go from f/2.8 to f/2. Achieving this means the aperture has to increase by 41.4%. Keeping the same slope on the glass means the glass means the thickness increases by 41.4% too. The result is that the weight of the glass must increase by 1.414^3 = 2.83x.
The structure that supports each lens has to be stiffer, and since it's going to be bigger, the mechanical bits get a lot heavier.
but that's not all....
Optical glass increases in price at roughly the fourth power of the aperture. This means the cost of glass has increased by 4x. Similarly, faster lenses demand tighter tolerances so the manufacturing costs increase. Say this quadruples too.
Suddenly a 70-200 weighs at least 10 lbs and material / manufacture costs $8000.
The price is very high, so the market size is now about 1/100 of the market size for the f/2.8 model. Amortise the development cost makes the lens even more expensive... say $10k.
If you think the numbers are wild, take a look at the Sigma 200-500 / 2.8. $26k and 35 lbs. Compare this with the 120-400/4.5-6. 10x as heavy and 26x more expensive.