In this thesis we study KMS weights on groupoid $C^{*}$-algebras. Our first objective is to study the structure of KMS weights on étale groupoid $C^{*}$-algebras. We extend a classical theorem by Neshveyev to KMS weights, allowing us to divide the description of KMS weights into the description of certain quasi-invariant measures and measurable fields of tracial states. We then investigate the properties of these measures and measurable fields of tracial states.

Afterwards we use the insight developed in this general description of KMS weights to consider the case where the groupoid $C^{*}$-algebra is the $C^{*}$-algebra of a higher-rank graph or a directed graph. This leads to a description of the KMS states for the gauge-actions on the Toeplitz and Cuntz Krieger algebras of finite higher-rank graphs. Joint with Klaus Thomsen we also describe the KMS states for generalised gauge-actions on finite digraphs, give a partial description of KMS weights for generalised gauge-actions on Cayley graphs and establish a connection between diagonal weights and diagonal actions.