Origins of Awake, etc.
Prefixes are added for numerous reasons. The a in awake and asleep appears to be attempts to create different grammatical forms of wake and sleep. They are Old English in origin. The a in assure and astound comes from the Latin ad, meaning to.
Besot, besmirch, and similar words have Old English roots. Again, the prefix is added for a number of reasons. Besot means to intoxocate, so besotted mean to be intoxicated. See the etymology of be- below.
be-
weak form of O.E. bi “by,” probably cognate with second syllable of Gk. amphi, L. ambi and originally meaning “about.” This sense naturally drifted into intensive (cf. bespatter “spatter about,” therefore “spatter very much”). Be- can also be privative (cf. behead), causative, or have just about any sense required. The prefix was productive 16c.-17c. in forming useful words, many of which have not survived, e.g. bethwack “to thrash soundly” (1555), betongue “to assail in speech, to scold” (1639).
This doesn’t apply to all such words. For more information, see http://www.etymonline.com
