Sounds like he's telling the other person not to become "emotionally invested" in them because they are not looking at them as being "the one" they want as a (life- mate).
"Don't start doodling your first name and his last name together....or dreaming about a future together..etc"
Like; in this instance simply means he enjoys spending time with her. In other words he looks at their situation as "hanging out" and not "dating". The "weird way" would be if he got butterflies in the stomach or his heart skips a beat whenever he's near her.
Some people use "weird way" to describe "Stalker behavior".
He wants to assure her that his "liking her" isn't that!
One man's opinion!:)