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.
I think he is being sarcastic in reply to his uncle's question. He is obviously sad about his father's very recent death which everyone else seems to have forgotten. In modern speak, the exchange: "How is it that the clouds still hang on you?" "Not so, my lord. I am too much i'the sun" would translate to something like: " Why are you still so upset?" "What? I'm not upset. I am soooo fantastic right now."