Gaussian mixture models (GMM) can be seen as the probabilistic counterparts of the kmeans clustering algorithm. Weighted kmeans takes a set of weighted samples and arranges the centroids according to weighted means of the data clusters, where the weights are the weights of the samples. I wonder if there is a GMMlike probabilistic counterpart of weighted kmeans.
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How about Clara, or even PAM? I think Clara is an interesting mix between kmeans and PAM. 


pKNN+AL (Jain and Kapoor, 2009) is a probabilistic modification of the KNN classifier. Given a set of points $\{x_1, \ldots, x_n\}$ from $\mathbb{R}^d$, labels $\{y_1, \ldots, y_n\}$ from $[1,C]$, and a Mercer kernel $K$, the probability of $x$ belonging to class $c$ is $$\frac{\frac{1}{n_c} \sum_{\{i : y_i = c\}} K(x, x_i)}{\sum_{t=1}^C \frac{1}{n_t} \sum_{\{i : y_i = c\}} K(x, x_i)}$$ where $n_c$ is the number of $x_i$ that belong to class $c$. It is also an active learning algorithm and comes with a MATLAB implementation. 


Are you looking for a GMM with weighted samples? Please see my answer 

