Origins of the "‑cede/‑sede/‑ceed" suffix

The different spelling of 'supersede' is appropriate because it is not derived from the same source as the others.

Supersede is derived from super (over) + sedere (to sit).
Proceed is derived from pro (forward) + cedere (to go).

Here is a comment from the Oxford dictionary on the spelling confusion of supersede:

The standard spelling is supersede rather than supercede. The word is derived from the Latin verb supersedere but has been influenced by the presence of other words in English spelled with a c, such as intercede and accede. The c spelling is recorded as early as the 16th century; although still generally regarded as incorrect, it is now entered without comment in some modern dictionaries

The -ceed/-cede suffixes are just spelling variations, all having derived from the verb cedere (to go/yield). The variation used appears to depend on the period that the word entered the English language:

• exceed; 1325-75
• succeed; 1325-75
• proceed; 1350-1400
• accede; 1400-50
• recede; 1470–80
• concede; 1625–35

There is one more exception that has nothing to do with Latin: the past tense of the informal verb to emcee is spelled emceed.