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As large amounts of data are circulated both from users to a cloud server and between users, there is a critical need for privately aggregating the shared data. This paper considers the problem of private weighted sum aggregation with secret weights, where an aggregator wants to compute the weighted sum of the local data of some agents. Depending on the privacy requirements posed on the weights, there are different secure multi-party computation schemes exploiting the information structure. First, when each agent has a local private value and a local private weight, we review private sum aggregation schemes. Second, we discuss how to extend the previous schemes for when the agents have a local private value, but the aggregator holds the corresponding weights. Third, we treat a more general case where the agents have their local private values, but the weights are known neither by the agents nor by the aggregator; they are generated by a system operator, who wants to keep them private. We give a solution where aggregator obliviousness is achieved, even under collusion between the participants, and we show how to obtain a more efficient communication and computation strategy for multi-dimensional data, by batching the data into fewer ciphertexts. Finally, we implement our schemes and discuss the numerical results and efficiency improvements.