"And the Sheen of their spears was like stars on the sea," How does the meter in this line emphasize this use of alliteration?
The meter of this line is anapestic tetrameter. Basically the line can be broken down into to four feet and each foot then consists of two unstressed syllables followed by a stressed syllable (in our minds, this foot might sound as such: da, da, DUM). This foot is called an anapest.
The alliteration of the 's' sound at the beginning of sheen, spears, stars, and sea is emphasized because those sounds all happen in the line at the end of each foot, in other words they fall on the stressed syllable of the line.
Given that every third syllable starts with the same sound, the meter serves to emphasize the effect of the alliteration. Because of the way you read it, you cannot help but feel the alliteration and if the repetitions of the beginning S sounds were on varying syllables, it wouldn't be as clear.