Dragons vs Balrogs

Now I must tell you my main reasons for my belief in dragon's magical eyesight. Now if you say that only Glaurung had the power to cast spells and such, then this proof is useless. But if you think all dragons can do what Glaurung did, then I can't see how you will refute it.

Glaurung constrained Nienor to gaze into his eyes. He must have had a reason for that, why else would he want to do it? Just to terrify her? I think that he did that so that he could cast the spell upon her. Turin was frozen by his gaze, and not until the Dragon had broken their eyesight connection did he snap out of it. Glaurung wouldn't maintain the steady gaze unless he had a good reason for it, as there were probably many other more useful things he could do at the moment then stare at Turin.

Now for the capstone of my theory. If the eyesight wasn't important, then Smaug surely would have cast a spell on Bilbo. Bilbo was invisible, and if it weren't for this, Smaug would have used his spells to defeat him. But as it was, he couldn't.

Even if the magic isn't in the eyes, obviously it is channeled through them.