  We give a detailed explicit computation of weights of Kontsevich graphs which
arise from connection and curvature terms within the globalization picture for
the special case of symplectic manifolds. We will show how the weights for the
curvature graphs can be explicitly expressed in terms of the hypergeometric
function as well as by a much simpler formula combining it with the explicit
expression for the weights of its underlined connection graphs. Moreover, we
consider the case of a cotangent bundle, which will simplify the curvature
expression significantly.
