Here's the cockpit of the F-4E:
The Main Panel NO7 says "Radar Scope" and when you put your mouse cursor on that "magician globe", the X-Plane 8.15 tooltip says "Weather Radar". So, what is that overly "oversized weather radar scope"?
The F-4 radar was a low PRF pulse radar, designed to search for, acquire, and track other airborne aircraft, and then provide guidance for Aim-7 Sparrow air-to-air missiles. It also had a ground mapping capability, and a capability to detect and display severe weather, but it was primarily designed for air-to-air combat.
Later models of the F-4 had an more modern radar, (installed in the German F-4F for example) which was a high PRF pulse Doppler system, and had improved capabilities, but I don't know whether they still had a weather mapping capability. I would be surprised if they did not.