the sun.

There is at least a double meaning to Hamlet's reply. One is that he dislikes having Claudius constantly referring him as his son, since he obviously does not like being forced to have more than one father--especially while he is still mourning his first one. He also means that he is getting too much exposure, too much royal attention. He is being forced to attend this big reception party because Claudius wants to make it appear as if Hamlet approves of being cheated out of his birthright to inherit his father's throne and approves of his mother's marriage to his uncle, who is now both his uncle and his father. Hamlet wants to return to school at Wittenberg, but Claudius won't let him go because he is fearful and suspicious of his moody stepson and wants to be able to keep him under surveillance.

Hamlet may also be implying that he has nothing to do but sit around outdoors, or perhaps go riding, because he can't study and has no useful function to perform at the castle. In this respect he resembles Orlando in Shakespeare's As You Like It, who complains to his elder brother that he is kept in ignorance, dependence and poverty when he should be improving himself through study or useful employment.

Hamlet is being sarcastic in regards to his new relationship with Claudius. Two months ago, Claudius was his uncle, now he is Hamlet's step-father. That is kind of mind-boggling and gross to us, and it undoubtedly is to Hamlet as well.  His first line, an aside, is "a little more than kin and less than kind." He is specifically talking about this change in their relationship.  When he says he is "too much in the sun" of course he is punning sun/son. He is saying he is too much a son now that Claudius has married his mother so soon after the death of his father. In several lines in this scene, Claudius calls Hamlet his son, which only serves to highlight Hamlet's attitude about all of this.  Throughout the play, Hamlet feels dirtied by the corruption of Denmark -- a theme that starts with his first lines.

This line from Act I, Scene II is actually a play on words. Claudius has asked Hamlet "How is it that the clouds still hang on you?" In other words, why are you still so sad? Hamlet's reply, is that he is "too much in the sun" but really means, he is still to much of a "SON" and is suffering grief over his father's death. Both Claudius and Gertrude seem to be unaware of Hamlet's pun, as both try to tell him to stop mourning for his father. Neither seems to realize that they have increased Hamlet's grief by marrying so soon after his father's death and their insensitivity is heightened by the fact that both say he has mourned too long. However, it has been less than two months since his father's untimely death and he still feels the sadness any son would feel at the loss of a father.