At the equinoxes, the difference between spring and neap tides is larger. At the solstices, the difference between spring and neap tides is smaller.
The TC for the spring tide on Wed 22 Feb is 112. The TC for the neap tide a week later on Wed 1 Mar is 28. This is a difference of 84.
The TC for the spring tide on Mon 5 Jun is 87. The TC for the neap tide a week later on Mon 12 Jun is 57. This is a difference of 30.
This difference is because the distance between the earth and the sun is smallest at the equinoxes and largest at the solstices:
The angle of the moon to the earth also changes. This affects the tide too. The animation below illustrates this effect:
oceanservice.noaa.gov/education/tutorial_tides/tides04_angle.html
The apogee and perigee of the moon, and the aphelion and perihelion of the sun have an affect but they do not cause of the large spring tides at the equinoxes and the small spring tides at the solstices.
This is my understanding at least. Please correct me if I am wrong.