  By using representation theory of the elliptic quantum group U_{q,p}(sl_N^),
we present a systematic method of deriving the weight functions. The resultant
sl_N type elliptic weight functions are new and give elliptic and dynamical
analogues of those obtained in the trigonometric case. We then discuss some
basic properties of the elliptic weight functions. We also present an explicit
formula for formal elliptic hypergeometric integral solution to the face type,
i.e. dynamical, elliptic q-KZ equation.
