The Poetry Foundation website categorizes Shakespeare's Sonnet XXXIII under the following categories--Living, love, landcapes and pastorals, time and brevity, nature, relationships, and "realistic & complicated" poetry. Just looking at that list, we can infer that the true message of this poem, and hence the theme, involve more than just musings about the weather.
Take a glance at the eNotes reference for this poem, which provides a nice modern language paraphrase to help us navigate Shakespeare's riddle. The essential verse to understand when deriving this poem's theme is "Even so my sun one early morn did shine" (9). While the first two quatrains deal with literal weather--sometimes the sun is just beautifully shining and then the clouds come and cover it up without warning--this new section of the poem goes into metaphorical territory. Shakespeare is now talking about "his sun," which was shining just like the real one. We can interpret this to be an inner spirit, positivity... the "light within", so to speak. The sonnet goes on to compare the natural world with our inner light: sometimes that gets clouded, too.
The final couplet reveals the theme we are meant to derive from all of this (and, by the way, the last two lines of a sonnet are typically supposed to contain the main revelation of the poem). They read "Yet him for this my love no whit disdaineth;/Suns of the world may stain when heaven's sun staineth" (13-14). In other words, it's ok that sometimes our spirits (the "suns of the world") can't shine to the fullest. Since the sun itself can be clouded over, we shouldn't love our own selves less because of intermittent "cloudy" periods in our lives. Clouds will pass, and we will shine again!