Obsequious means obedient or attentive in an ingratiating or servile manner. Submissive or compliant. Miriam Webster defines it as "too eager to help or obey someone important".

Some uses of this word would be:

"Nash's other hand flashed forward a lighter with the obsequious speed of a motor salesman". Ian Fleming, From Russia With Love, 1957

She's constantly followed by obsequious assistants, who will do anything she asks.

More Info: www.miriamwebster.com