1. A block-based storage service of a provider network, comprising: one or more computing devices implementing a configuration manager for the block-based storage service, the configuration manager configured to: determine one or more configuration changes for a data volume hosted for a client in the block-based storage service according to one or more data volume offerings of the block-based storage service based, at least in part, on historical client utilization of the data volume; and reconfigure the data volume to a new configuration according to the determined one or more configuration changes such that subsequent utilization of the data volume is provided according to the new configuration, wherein reconfiguration of the data volume comprises: update of one or more hosts of the data volume to provide the new configuration, or performance of one or more migration operations to relocate the data volume to one or more different hosts capable of providing the new configuration, or migration of the data volume to another storage service implemented as part of the provider network.