Where does “sille” come from?

sille (Middle English) comes from Old English syll, from Proto-Germanic sulī, from Proto-Indo-European sēl- — to calm, quiet, be favourable.

Ancestry of “sille”, step by step

Step	Language	Word	Meaning
1	Old English	syll	a beam that serves as a foundation or support,...
2	Proto-Germanic	sulī	balk, bar, threshold, sill
3	Proto-Indo-European	sēl-	to calm, quiet, be favourable

sille — Etymology, Origin & Word History | Etymology Explorer