It is not weaker it is about the wavelength of the C band. For parabolic reflectors the directivity equation is G=10*log_10(k*((pi*D)/lambda)^2)) where k= efficiency factor generally between 0.5-0.8, D= diameter of the reflector, lambda=speed of light/frequency.
Now you can get the idea that when the frequency goes up wavelength goes down, because lambda is in denumerator of the equation when lambda goes down gain increases. So for the same reflector size, C band has the lowest gain.
So lets say you want to get a 30 dBi gain from your antenna at C band and Ka band.Assuming both of your antennas have %70 efficiency(k=0.7) you would need 1.25m antenna for Ka band transmission at 29GHz , for the same gain you would need a 6.3 meter antenna for C band transmission at 5750 MHz.