There should be variable activities depending on plant species. This question may also be asked as What is the benefit of night for the plants (C3, C4, CAM, C3-C4 etc).
1) Depending on the particular plant species the night duration, as being part of the whole photoperiod, can be determinant for blooming process.
2) Regarding CAM plants which open their stomata during the night, the benefit is CO2 assimilation with low transpiration.
3) Considering that respiration occurs during both daytime and night, I think that it is difficult to reflect a benefit during the night. Moreover, the usually lower temperatures during the night (especially the temperatures lower than 10oC) may reduce respiration.
Days/nights environmental cues can also involve in plant CIRCADIAN CLOCKS, which is important for plants' development. Some gene transcripts (mRNAs) only accumulate late at the day. For example, the transcription of the CONSTANS (CO) gene is clock regulated so that CO mRNA only accumulates late in the day and is translated after dusk. See attached paper.
During the daytime plants need light to live, in order to be able to produce sugars and carbohydrates as well as oxygen. However at night they can't produce these. In order to survive this period without light, they breathe, in a way similar to human beings--by using oxygen and carbohydrates.