There are several rules governing the use of commas, but there is also a lot freedom.
Webster's Third New International Dictionary begins their article on commas with:
Of all the marks of punctuation the comma offers the most difficulty in use and the widest range for individual choice. Though often marking rhetorical or elocutionary pauses, the comma is used primarily to separate or to set off in a group. It sometimes distinguishes nonrestrictive modifiers from restrictive modifiers.
More to the example at hand, they say:
Commas set off transitional words and expressions (as on the contrary, on the other hand, consequently, furthermore, moreover, nevertheless, therefore) whenever they are or would be spoken with the adjacent rising or sustained pauses that indicate subordinate matter <The question, however, remains unsettled.> <Nevertheless, we shall go.> <On the contrary, under the rules a vote is in order.>
I would say use a comma before
either if you feel there would be a pause there if the sentence were spoken.
Either in this sentence is used as an adverb and means
likewise or
also. It is used as an intensifier following the initial negative phrase. There would have to have been a previous statement to justify
either. Also, I think the word
being is ellipted.
He was left weak by childhood illnesses. [Being] not the biggest boy in the world[,] either, at five feet two inches, he began working out.
To me, the use of the first comma is debatable. In this construction I would tend to omit it because
either seems to belong with the rest of the negative phrase. Again from
Webster's:
<You'll not go far in life and you won't be happy either. --W. J. Reilly>.