milksop is a very similar word, which Merriam-Webster defines as
a weak boy or man
or
an unmanly man
The etymology given is
Middle English, literally, bread soaked in milk. First Known Use: 14th century
A Google search for milksop provides the synonyms:
namby-pamby, coward, weakling, Milquetoast
I have found no firm agreement on whether the term milksop for a weak person derives from that person's similarity to the dish of milksop (bland, insipid, weak), or that the person resembles the sort of individual who would be fed milksop (an infant, or sickly person). It is certainly one or the other.
There is a long discussion on the etymology of milksop in Current Methods in Historical Semantics(pages 26-29), which again reaches no firm conclusion on this matter, as far as my understanding of the passage goes.
However, it is certain that there is no development of milk itself as being a negative term.
Incidentally, sop itself appears to come from soup as indicated in The Register of the Privy Council of Scotland, Volume 6 (1599-1604), referring to a breakfast in 1602.
Unless milk is implied in the “ sowpe” in which the “quhyte breid" [white bread] or the “ait laif” [oat loaf] was to be presented, there is no mention whatever of that article. Porridge also, which we should have expected at the bursars' table, seems to be completely absent; for it is difficult to construe "ain ait laif in a sowpe" [one oat loaf in a soup] as meaning ordinary porridge even without milk. What we see is some kind of sop of oat bread for the bursars, and a similar sop of wheat bread for the masters, with cold meat and ale in addition. On this they began the day in Glasgow in the year 1602, - the breakfast of the Glasgow Professors not differing much, it may be assumed from that on which Shakespeare and other well-remembered Englishmen of that time were in the habit of beginning the day in London.
This passage may suggest that the nature of the dish is what is referred to when milksop was first used as an insult, as bursars, masters and professors at Glasgow, in addition to Shakespeare and other London gentlemen would not take kindly to being considered sickly by dint of their choice of breakfast dish. But, I concede that this is not proof and I consider the matter to be open to debate.