より is a comparative term. So 今+より = compared to now/~than now, inferring "further along in time", or in this case "when I/you get older/bigger" as modified by "大きくなって"
As for "大きくなって", this is the い-adj. 大きい (meaning "big, large") that when used to modify a verb, the final い is changed to く (becoming the adverbial form) and added to the verb.
The confusion may lie in that we're taught that 大き is a な-adjective, so you would never see 大きく. But the reality is that 大きい also exists and is used that way. The only thing that keeps me sane is the ”すずめの兄弟” song that has a repeating phrase of "...大きくなったら何になる？” It was very popular in Japan when I was a beginning 日本語 student in Tokyo. It was hard to escape as it flooded the airwaves for nearly a year. So I suppose that I was just beaten into submission... Once you hear the song you'll never be able to unhear it. Try it. It will fix your dilemma.