What is the proper response to I love you? Is it "I love you too" or "I too love you" ?
I too = I, in addition to another person or persons
I, too, am wearing a blue shirt.
The sentence above implies that I am not the only person wearing a blue shirt. I am one of the people wearing blue shirts.
I am wearing a blue shirt too.
This form is ambiguous, and the ambiguity can be resolved only by the context. It could mean that my trousers, say, or my necktie, is blue and so is my shirt. Or it could mean that I am not the only person wearing a blue shirt; I am one of the people wearing blue shirts.
In speech, the intonation pattern would disambiguate:
I'm wearing a blue shirt too. (I'm one of the people wearing blue shirts)
I'm wearing a blue shirt too. (My shirt is not the only blue thing I'm wearing)
I too love you.
Too here modifies I, implying there are other people that love you besides "I". It can't modify any other word.
I love you too
Too can modify any other word in this sentence. In speech, the word stressed indicates which is modified. In text, you have to pay attention to context.
I love you too = I + other people love you.
I love you too = I love + other actions to you.
I love you too = I love you + other people.
I love you too = I love you in the same manner as someone else loves you. 90% of the time the "someone else" is whoever "you" is in the sentence.
"I love you too" is pretty idiomatic in English and the last meaning is usually what these sequence of words mean - but the way it is said or context can make the other meanings possible.
To only say
I love you too.
after someone has professed their love for you is a bit uninspired.
If you are feeling playful, you might say
I love you (right) back.
I love you more.
Not as much as I love you!
If you say
I too love you.
Though correct grammatically, may not be what you mean romantically.
It only means that you are one of possibly many admirers.
" I love you, too." should be the correct way of saying, of writing; this "too", means "also", "in the same manner or way", "likewise". It's more colloquial, more popularly used than to say "I also love you". "I love you the same", "I just love you in that way", which might sound, "perfunctory", "bookish" or "sophisticated, educated" or "academic". "I too love you" is "ackward", a faulty construction that not even Popeye would say never.