This is the 8263rd most frequent Japanese word.
座り
"座り" means "sitting" or "the act/state of sitting."
Here, '座り続ける' (suwari tsuzukeru) combines '座り' as a noun form with '続ける' (continuing), discussing the extended act of sitting, hence expressing duration and habitualness.
長時間座り続けることは健康に良くありません。
Continuously sitting for a long time isn't good for your health.
The word '座り' (suwari) is derived from the verb '座る' (suwaru), meaning 'to sit'. Here, '座りました' is the past tense form, indicating a completed action of sitting.
彼は椅子に座りました。
He sat on the chair.
'座り' (suwari) in this form is part of '座って', the conjunctive form used for polite request, derived from '座る'. It reflects the act of sitting as part of a question.