Concurrent constraint programming (CCP) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioral equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for CCP, and a CCP partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimilarity is a central behavioral equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milner's reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for CCP. We give an alternative reduction from weak CCP bisimilarity to the strong one that allows us to use the CCP partition refinement algorithm for deciding this equivalence.