okay, if someone said, "blue is my favorite color," you couldn't reply "I am too." "Me too is an idiom, and so evidently this is the way they say it. They are two different things
Contrarily, if someone says "I'm sick of having to translate sentences without context" you COULD reply "I am too".
vậy means "like this", "in this manner". you do need it, otherwise there is definitely something missing.
I am also like this = Me too