From Middle High German sīt, early apocope of sīde, from Old High German sīda, northern variant of sīta, from Proto-Germanic *sīdǭ. Cognate with German Seite, Dutch zij(de), English side, Icelandic síða.
Luxembourgish, like most of West Central German, does not exhibit the shift d → t (the plural Säiten is analogous). Accordingly the expected form would be *Seit with the so-called “short diphthong” as in leiden, reiden, zeideg. The form Säit with the “long diphthong” points to apocope of the final -e before the general development, thus Middle High German sīt, which is indeed widely attested.
Säit f (plural Säiten)
Borrowed from German Saite, from Old High German seita. Formally adapted to etymology 1 because the German word is homophonous with Seite. If it had been inherited, the Luxembourgish form would be *Seet. Compare similarly Läich (“spawn”).
Säit f (plural Säiten)