You shouldn't really let your banana ever get dry. They love to stay moist (but not sodden) at all times. I grow Musa basjoo outside year around here in northeast TN and they can't get too much water or fertilizer!

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Weak stems is indicitive of not enough direct light. Move it outdoors in a shady area for a couple of weeks, then move it to full sun, and keep it moist. It should improve dramatically. Are you fertilizing it? They require lots of water and fertilizer and light to grow and produce pups.

It's a bit early, but perhaps it is slowing down for winter.
What size pot is this in?
I think some summer outdoor time would be good - start it off with some shade.

seahorse

There may not be any outdoor space available for a New York City banana. Agreed though, if a sunny outdoor break were possible, this would be beneficial.

It's always hard to give watering recommendations when you don't know what kind of soil or pot size the plant has. The banana could be pot-bound, the soil could be soggy and sour even with once-weekly watering, it could be too dry etc.
Sometimes repotting and rejuvenating the soil can be beneficial.