  We establish a determinant formula for the bilinear form associated with the
elliptic hypergeometric integrals of type $BC_n$ by studying the structure of
$q$-difference equations to be satisfied by them. The determinant formula is
proved by combining the $q$-difference equations of the determinant and its
asymptotic analysis along the singularities. The elliptic interpolation
functions of type $BC_n$ are essentially used in the study of the
$q$-difference equations.
