[dan-robertson]

This usage in modern words traces its way back to an analogy to metaphysics transcending physics. In Greek, meta meant with or after and the book metaphysics was named because it came after physics. The Greek word has related etymology to the Old English mið (or mid) which was subsumed into the meaning of with (an original usage of the word with can be found in the word withstanding).

One may notice words that come from the original Greek meaning if they start with meth or met + some vowel except a (although words with this original sense) and modern words (eg in zoology) also exist based on the old Greek meaning, as well as other irregular constructions (in geology words beginning with meta relate to metamorphosis).

Notwithstanding the broken origins of the sense you describe, it is indeed a good word/prefix.

[pineaux]

Also a nice fact: "Mit" is still the German word for "with". So is "met", but that's in dutch. The Danes use the word: "med".