Everyone knows that labour in British English is labor in American English.
However, a cursory examination of a dictionary shows the words collabourate and collabourator, derived from the mentioned word labour, do not exist in British English.
Why not?
Bearing in mind that orthography is to some degree capricious, nonetheless the reason "why not?" can be affirmed in this case. Simply, 'collaborate' is a much later borrowing than 'labour', and draws its spelling from different etymons. 'Collaborate', in short, is not derived from 'labour' per se.
For 'collaborate', the OED Online gives this etymology,
< modern French collaborer, or its original, Latin collabōrāre
and the first attestation of the word's use is from 1871:
1871 J. H. Appleton Life & Lit. Relics (1881) 25 The collaborators of the Revue critique, especially those who collaborate for the Academy.
For 'labour', however, the same source gives this etymology:
Etymology: Of multiple origins. Partly a borrowing from French. Partly a borrowing from Latin.
Etymons: French labure; Latin labor.
< Anglo-Norman labure, Anglo-Norman and Old French labur, labor, Anglo-Norman and Old French, Middle French labour, Old French, Middle French labeur (French labeur) trouble, effort, affliction, misfortune (first half of the 12th cent. in Anglo-Norman), hard work (1155), burden, task (c1170 or earlier in Anglo-Norman), suffering (c1270 or earlier in Anglo-Norman), outcome, product, or result of work (1283), ....
In the case of 'labour', the earliest attested uses in English occurred in the 1300s, much earlier than the appearance of 'collaborate' in the 1800s.
The spelling of 'labour' with 'u', then, is a consequence of its earlier borrowing from etymons with at least one spelling in 'u'; 'collaborate', on the other hand, was borrowed at a much later date and derives from etymons without the spelling in 'u'.
