Personally, repeating the same songs every week really isn't something
I prefer.

I was placed in a no-win situation like this a long while ago:

I have repeated tunes in the distant past at some of the venues I
played (sing-around pubs), although I was reluctant to do so.
Some regular attendees would ask me for the same songs every time, and late arrivals would ask for one or two certain songs that I
already played. On occasion, I might have repeated one at the end of my set, but no more than that in the same night.

I would repeat one or two "staple songs" week after week, because somebody was always asking for those songs, but I would mix it up a bit with the rest of my set, always trying to fit in different songs each week.

At one point, I quit for quite some time and avoided the particular
places where I would always be asked for the same songs. I couldn't
keep repeating them, because some regular attendees might become
bored and I know that I was bored of those songs. However, I
couldn't say no, because other regular attendees or late arrivals
who missed a particular song would be disappointed. I couldn't
decide who would win.

I was moving anyway, and wouldn't have been within a reasonable distance to play shows often in the area, but I let people who used to hear me play know that I would be moving soon. That sort of saved me from making the decision of whether I should repeat the same songs week after week, and lose attendees who were getting somewhat bored, OR losing attendees for not playing the songs they wanted to hear; though it was the same people, same songs, every time.

In the aftermath, I determined that I might keep a one or two
"temporary staple song" system, with one being the opener. But, I would only do so once per venue until I've played an entire cycle of
the venues I would normally play, then I would pick one or two
different songs, and use them throughout the cycle.
It would normally depend on how many songs are in the set. If I was
playing a ten song set, one or two staple songs, but 15-20, I would
double it; and I would always mix up the order they're placed in the
set at random.