I base the grouping on the diameter of the front element of the lens
Guestimate price of a modern 500mm f/5.6 IS
$2,200 100-400 f/4.5-5.6 IS II; 1.59kg
$2,300 70-200mm f/2.8 IS II
89.29mm (theoretical price & weight)
$4,000-5,000 500mm f/5.6 IS
$2,000 Sigma 150-600mm f5.0-6.3; 2.86kg
$6,000 200mm f/2.0 IS
$6,470 400mm f/4.0 DO IS; 1.94kg
$11,800 200-400mm f/4.0 IS
$6,600 300mm f/2.8 IS II
$9,500 500mm f/4.0 IS II; 3.19kg
Within context f/5.6 and smaller f-numbers are equated to lower price tags but the front element's diameter is a better indicator for pricing.
Now why does Canon make five lenses with a maximum focal length of 400mm and only one lens whose maximum focal length is 500mm, 600mm and 800mm?
Pretty much demand is not large enough for more than one f-number at these focal lengths.
I was also hoping for a 500mm f/5.6 as 400mm f/5.6 is largely useless in the Philippines for birds in the wild.
Now, the lens would sell for 1/2 of a 500mm f/4 IS II at below 2kg. As for height, length and depth I cannot really say.
Sigma on the other hand would be best in the position to offer such a lens at the price you are asking for.
In fact Sigma does make a 500mm f/4.5 without OS at $5,000 at 3.09kg.