This really is the answer to your really tough question.

Actually, it's not such a tough question. I just wanted to use "really" in two ways, because that's what this question is about. A student is asking:

"According to my English text, it says the position of 'really' is a matter of emphasis. So I think there is a difference between 'it really is weird' and 'it is really weird'. However, I don't know the difference. Could you tell me the difference?"

変 - strange; odd; peculiar; weird; curious; queer; eccentric; funny; suspicious; fishy; (definition from Edict)

Yes, there is a difference between these two.

• It really is weird. = Truthfully, it is weird. <- "really" modifies "is"
• It is really weird. = It is very very weird. <- "really" modifies "weird"

Look at these example conversations:

A: It's hot outside.
B: You're crazy. It's the middle of winter.
A: No, I'm serious. It really is hot.

A: It's 45 degrees outside.
B: Wow! It's really hot!

The food in the photo really is something I cooked. That's stir-fried broccoli and carrots with vegetarian oyster sauce. The plate in the back is stir-fried fried tofu and bean sprouts with sesame sauce. It was really delicious, too.

I'm really glad that you are really paying attention to grammar! Everyone really should pay close attention like that.