He only writes late at night. What does it mean?

Late messages tell you when contact is happening, not why. A schedule, habit or preference may explain the hour; the content and any daytime plans provide more context. The first question for you is whether this timing works.

If you want contact outside the night, a specific daytime invitation makes that visible. A different time that works for both of you is useful information. There is no need to delay an answer just to provoke a response.