'Sit' is PIE *sed- — one of the oldest verbs in any language, with cognates in every IE branch.
To be in a position in which one's weight is supported by one's buttocks rather than one's feet; to be in a particular position or state.
From Old English 'sittan' (to sit, to occupy a seat, to remain in place, to be situated), from Proto-Germanic *sitjaną (to sit), from PIE *sed- (to sit). This root is among the most ancient and universally reconstructed in the entire Indo-European family, appearing with near-identical consonantism across every major branch. Latin produced 'sedēre' (to sit), giving 'sedentary,' 'session,' 'sedate,' 'preside,' and 'reside.' Greek 'hédra' (seat, base) gave 'cathedral' (the chair of a bishop) and 'Sanhedrin.' Sanskrit 'sīdati' (sits) preserves the root almost
English 'sit' and 'set' are an ancient causative pair: 'sit' means 'to be seated' (intransitive) and 'set' means 'to cause to sit, to place' (transitive). This same sit/set distinction goes back to Proto-Germanic and ultimately to PIE, where causative verbs were formed by changing the vowel grade. The pair mirrors 'lie/lay,' 'rise/raise,' and 'fall/fell' — all ancient intransitive/causative doublets.