weilen
to dwell
To stay or remain in a place for a certain period of time. The word is mostly used in elevated or poetic language.
Der König weilte für drei Tage in der Stadt.
The king dwelled in the city for three days.

to dwell
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to dwell
To stay or remain in a place for a certain period of time. The word is mostly used in elevated or poetic language.
Der König weilte für drei Tage in der Stadt.
The king dwelled in the city for three days.

The verb 'weilen' (to dwell/stay) is closely related to the noun 'die Weile' (a while, an indefinite period of time). So 'weilen' literally means to spend a while in a place.
Er weilte eine ganze Weile am Fenster und blickte hinaus.
He dwelled at the window for quite a while and looked outside.
'Weilen' (to dwell/stay) is an elevated, almost poetic word. It is not used in normal everyday language. It fits formal occasions or literary texts.
Der Dichter weilte oft an diesem See, um Inspiration zu finden.
The poet often dwelled by this lake to find inspiration.
The phrase 'nicht mehr unter uns weilen' (to no longer be among us) is a very formal and indirect paraphrase for a person's death. It is often used in obituaries or memorial speeches.
Der geschätzte Kollege weilt seit letztem Jahr nicht mehr unter uns.
The esteemed colleague has no longer been among us since last year.
to stay / remain
'bleiben' and 'weilen' can both mean that someone is in a place for a while. The most important difference is style. 'bleiben' is the normal everyday word and fits almost always. 'weilen' sounds elevated, solemn, or poetic and is rarely used in normal conversations. If you simply want to say that someone is not leaving or is in a place, 'bleiben' is more natural. 'weilen' is more suitable in written texts, speeches, or deliberately elegant language.

Während seiner Reise weilt der Autor einige Tage in Wien.
During his trip, the author stays in Vienna for a few days.
Mein Nachbar bleibt heute zu Hause, weil er krank ist.
My neighbor is staying at home today because he is sick.