Glen and all,
What about the following etymology of
<basileus>?
Greek names in -la:(w)os < *lah2wos 'men (esp. under arms)'
were often truncated to <-leus> or even <-los>. There are several
attested names of the "bahuvrihi" type *X(-i)-la:wos with the etymological
meaning "he whose lâos has X", e.g. (apparently) Akhil(l)eus < *akhi-la:wos
'he who makes the lâos grieve' (literally "grief-lâos") or Kharillos <
*khari-la:wos 'who makes the lâos rejoice' ("delight-lâos"). What if
<basileus> is simply a truncated variant of *gWasi-la:wos (*gWasi- <
*gWmti- 'motion, step, progress' = <basis>) 'he who has the lâos
going/marching', i.e. 'the man in charge, commander'? Truncation, as in the
case of personal names, is explicable as due to frequent use, perhaps as a term
of respectful address, something like "boss", or "guv'nor".
Piotr