Tight is used as an adverb following verbs that denote a process of closure or constriction, as squeeze, shut, close, tie, and hold. In this use it is subtly distinct from the adverb tightly.
Tight denotes the state resulting from the process, whereas tightly denotes the manner of its application. As such, tight is more appropriate when the focus is on a state that endures for some time after the activity has ended. The sentence She closed up the house tight suggests preparation for an impending blizzard.
By the same token, it is more natural to say The windows were frozen tight than The windows were frozen tightly, since in this case the tightness of the seal is not likely to be the result of the manner in which the windows were frozen. With a few verbs tight is used idiomatically as an intensive and is the only possible form: sleep tight; sit tight.
Tight can be used only following the verb: The house was shut tight (not tight shut).(from the American Heritage Dictionary)