Does the pejorative meaning of the word Silly “to pray, holy” have any relation with the word Wasilas “priest” in ancient Greece?

OK. This is still A2A clearing out season. (I’m almost done, because for some reason Quora is throttling my unanswered legacy A2As.)

I’m not aware of basileus “ruler, king” being used in Ancient Greek to mean “priest”, or of any hint of Caesaropapism/conflation of the sacred and the secular in the word. I’m not an expert in the field, but I’m not aware of it. The fact that placenames around Mt Olympus now have Vasil– stems in them (as OP mentions in comment) doesn’t tell me anything about sacred rulership: those placenames can by default be assumed to be modern and referring to Byzantine emperors, or fairy tale kings.

I know that the word was written as qasireu in Linear B, and Wikipedia says the proto-Greek would be gʷatileus; the form is likely not Indo-European.

That makes it unlikely to be related to any of the other forms OP has adduced, which are Indo-European and spoken very far from Pelasgia: French sale, English sully, English silly, and Greek salos.

Well, the last one may be pre Greek too. But you can’t just chop off two syllables and a vowel and call the results cognate.

Going through:

• English sully < Proto-Germanic *suliwōną, *sulwōną, *sulwijaną ‎(“to sully, make dirty”), < Proto-Indo-European *sūl- ‎(“thick liquid, muck”). Cognate to soil.
• French sale “dirty” < Old Frankish *salo ‎(“dull, dirty grey”), from Proto-Germanic *salwaz ‎(“dusky, dark, muddy”), from Proto-Indo-European *salw-, *sal- ‎(“dirt, dirty”). That’s actually a bit of a surprise, I’d have thought they were the selfsame stem. The English cognate is sallow.
• English silly < Middle English seely, sēlī ‎(“blessed; good; innocent; weak; guileless; pitiful; lowly; punctual”) < Old English (ġe)sǣliġ ‎(“blessed; fortunate”) < Proto-Germanic *sēlīgaz < *sēliz < Proto-Indo-European *sōlh₂- ‎(“mercy, comfort”).
• Greek σαλός “silly, imbecile” (attested in Hesychius and scholia to Aristophanes; it is mediaeval Greek); Chantraine tentatively derives it from σάλος “disturbance, storm”, whose etymology is unknown. That would mean that salos originally meant something like “stormy”—or “disturbed”.

English silly and Greek salos are interesting in that they actually switched meanings in mediaeval Christianity, in a weird kind of way.

Silly started out meaning “blessed”, a meaning its German cognate selig retains. If you’re acting blessed according to the precepts of Christianity, that means that you’re acting guileless; that means you’re naive; that means you’re foolish; that means you’re silly.

Modern Greek had the same conclusion about acting guileless. The word that in Modern Greek means “guileless to the point of being simpleminded, too naive to live” is…

… agathos. The Ancient Greek for “good”.

But salos went the opposite way. It started meaning “disturbed”, and thence “imbecile”. In Bithynian Greek (which would date from after the 16th century), it came to mean a “baby”. (In the rest of Greek, mōron came to have that meaning.)

But in Mediaeval Orthodox Christianity, being mentally disturbed was taken as a sign of holiness. The salos is the figure who is only marginally better known in English under its Russian name, yurodivy (which pops up in exegeses of Shostakovich): it’s the Fool for Christ:

The yurodivy is a Holy Fool, one who acts intentionally foolish in the eyes of men. The term implies behaviour “which is caused neither by mistake nor by feeble-mindedness, but is deliberate, irritating, even provocative.”

In his book Holy Fools in Byzantium and Beyond, Ivanov described “holy fool” as a term for a person who “feigns insanity, pretends to be silly, or who provokes shock or outrage by his deliberate unruliness.” He explained that such conduct qualifies as holy foolery only if the audience believes that the individual is sane, moral, and pious. The Eastern Orthodox Church holds that holy fools voluntarily take up the guise of insanity in order to conceal their perfection from the world, and thus avoid praise.

Some characteristics that were commonly seen in holy fools were going around half-naked, being homeless, speaking in riddles, being believed to be clairvoyant and a prophet, and occasionally being disruptive and challenging to the point of seeming immoral (though always to make a point.

So silly described someone so holy they were considered mentally disturbed. And salos described someone so mentally disturbed they were considered to be holy.