2 represents balance, and possibly 8...

2 is associated with Libra, the sign of balance and harmony as well as judgement. Though 8 is associated with Capricorn, it is said to represent in it's two circles, heaven and earth, spirit and matter, which in many ways represents finding a balance between materialism and aestheticism or rejecting the material.

I've never heard of 69 being associated with balance. Turned on it's side it is the symbol for Cancer. It perhaps could also be seen that way as the yin yang symbol. Maybe that is why you are associating it with balance? In that way it is less about the numbers themselves and numbers as abstract symbols representing something else.

6, associated with Virgo or Cancer is family, community, the cosmic parent, comfort, and the arts. 9, associated with Aquarius, is humanitarianism, strength of feeling, theatre/drama. Added together they add back down to 6.