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We give an explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture as in [12] for symplectic manifolds. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly. Contents 1. Introduction 1.1. Motivation 1.2. Notions of Formal Geometry Acknowledgements 2. Computation of Kontsevich Weights 2.1. Case 1: No Boundary Vertices 2.2. Case 2: One Boundary Vertex 2.3. Case 3: Two Boundary Vertices 3. Including the Weights 3.1. The Product P (Tφ * π) The Connection 1-form1 Endowed with the zero differential and the Schouten-Nijenhuis bracket.2 Endowed with the Hochschild differential and the Gerstenhaber bracket.