Yes, as hanoun said, you'd use 大きい (ookii) as the adjective, "big"
大好き is a na-adjective meaning "to like very much." The kanji 大 is pronounced, "dai," in this context. So, the whole would would be, "daisuki."
"Dai," and "tai," are on-readings of that kanji. Normally, a kanji's on-reading isn't used when the kanji itself stands alone as a word. They are mostly used in compounds. There always are some exceptions, of course.
Here are some examples:
書
図書館 to SHO kan, library
書く kaku, to write
Sho--on-reading
Ka(ku)--kun reading
人
三人--san nin (when used as a counter, the on-reading "nin" is used)
日本人-Ni hon jin (when used as a suffix for nationality, the on reading "jin" is used
人-Hito, when used alone, it is just pronounced with it's kun-yomi, "hito."