A metamaterial that capitalizes on a double porosity architecture is introduced for controlling broadband acoustic energy suppression properties. When the metamaterial is subjected to static compressive stress, a global rotation of the internal metamaterial architecture is induced that softens the effective stiffness and results in a considerable means to tailor wave transmission and absorption properties. The influences of mass inclusions and compression constraints are examined by computational and experimental efforts. The results indicate that the mass inclusions and applied constraints can significantly impact the absorption and transmission properties of double porosity metamaterials, while the appropriate utilization of the underlying poroelastic media can further magnify these parametric influences. Based on the widespread implementation of compressed poroelastic media in applications, the results of this research uncover how internal metamaterial architecture and constraints may be exploited to enhance engineering noise control properties while using less poroelastic material mass.