As you can see in the title the words "weg" and "Weg" confused me somehow. Is the only difference between them the upper-/lowercase writing?
In written language, yes, unless you start your sentence with "weg" as in
Weg mit dir!
But in spoken language, the "e" in "Weg" is longer.
In terms of phonetics:
Weg, [veːk], close-mid, frontal, unrounded vowel
weg, [vɛk], open-mid, frontal, unrounded vowel
The comparative "lighter"
was attributed to the e in Weg by Emmanuel. [e] is technically closer to [i] than [ɛ] is, so if you perceive be [i] to be "lighter" than cat [æ] for instance, then I guess you could say so.
Although an example of a longer [ɛ], like Käse [ɛ:], shows us how length is a bigger factor here.
English examples for [e/ɛ] are hard to find. Maybe men for [ɛ] and a Scottish/Irish pronunciation of days for [e].
As mentioned before, "weg" and "Weg" are pronounced differently:
Weg, noun, [veːk]
weg, adverb, [vɛk]
Nonetheless, both words share a common etymology. The reason for the difference in pronunciation is the following:
In Middle High German, "weg/wec" [vɛk] had a short vowel and was used both for the adverb and the noun. When declining the noun, there was for example the plural "wege" ['vɛ.gə], also with a short vowel. In the transition from Middle High German to New High German, vowels in open syllables (no consonant at the end) were lengthened; i.e. one has the plural "wege" ['veː.gə] but still has the adverb and the singular noun "weg" [vɛk]. In New High German, the singular noun "weg" changed its pronunciation, per analogy to the long-voweled plural, from [vɛk] to [veːk]. It was not recognized by New High German speakers that the adverb "weg" once belonged to the same paradigm; thus it did not get the long vowel.