I thought that such a behaviour can be regarded as childish. In addition, as obsequiousness’ means ‘attentive to excessive degree’, how can the latter be correct ?
Obsequious has a direct synonymous meaning of the phrase “adulate her superiors”; there’s no doubt about that. If I had to guess my word for the blank, I would put adulation, simply. If someone is obsequious, it means they’re like a bootlicker, fig-shower, or have an overly fawning behaviour. I think you are looking at a part of the meaning of this word; look more closely for the complete meaning.
Petulant, too, has a -ve connotation, but that doesn’t match the semantic guess for the blank. Obsequiousness is almost a direct synonym for the abovementioned phrase.