In online slang, 大号 means your main/public account, while 小号 (xiǎohào) is your alt or secondary account. In clothing stores, sizes go: 小号 (S), 中号 (M), 大号 (L), 加大号 (XL).
memory
大 (big) + 号 (number/size) — the 'big size.' For the tuba, picture a big brass instrument with a big number on it.