Tight is used as an adverb following verbs that denote a process of closure or constriction, as squeeze, shut, close, tie, and hold, denoting the state resulting from the process, whereas tightly denotes the manner of its application.
The windows were frozen tight rather than tightly, since in this case the tightness of the seal is not likely to be the result of the manner in which they were frozen.
Tight can be used only following the verb: The house was shut tight or ...tightly shut.
The same dictionary distinguishes two senses for the adverb THIN, but the second one is in my opinion an adjective with the verb cut used copularly meaning "become"
- In a thin manner: Spread the varnish thin if you don't want it to wrinkle. Seed sown thin
- So as to be thin: Cut the cheese thin.
Why isn't tight an adjective as is dead in shoot someone dead?
Secondly, I don't fully grasp the distinction between tight(ly), especially regarding the example of the windows.
Finally, why can't shut be an adjective in the last example?