Suppose we have n-variable Boolean function (BF) and we know that the weight of a Balanced BF is $2^{n-1}$. The total number of BFs are $2^{2^n}$, Affine BFs are $2^{n+1}$ and Linear BFs are $2^n$. In general the number of Balanced BF will be greater than the combined number of Affine and Linear BF.
A Balanced BF outputs equal number of $1$s and $0$s.
Affine BF is defined as $f(x)= wx+c$, where $w,x \in F_{2}^n$ and $c \in F_{2}$. The additions whether in dot product or of $c$ are all mod 2 i.e. xor.
An Affine BF is called Linear if $c=0$
From the definitions of Linear and Affine we can deduce their number but I don't have any idea how to find the number of Balanced BF?