Cohen's kappa is a weighted average

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Conditional inequalities between Cohen's kappa and weighted kappas (2013, methodology): “Popular descriptive statistics for summarizing the agreement between two raters are Cohen’s unweighted kappa, denoted by κ [7,19,22,27,30–35], and Cohen’s weighted kappa, denoted by κw [4,8,28].”
Five ways to look at Cohen's kappa (2015, methodology): “Cohen’s kappa is the most commonly used statistic for assessing nominal agreement between two raters [1-7].”
The Matthews Correlation Coefficient (MCC) is More Informative Than Cohen’s Kappa and Brier Score in Binary Classification Assessment (2021, background): “Various authors later discovered that Cohen’s Kappa may be interpreted as chance-corrected version of various measures other than accuracy in Equation 4 [33].”
New interpretations of Cohen's kappa (2014, background): “The overall kappa is a weighted average of them category kappas [15–17].”