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Clinical ultrasound contrast agent microbubbles remain intravascular and are between 1-8 µm in diameter, with a volume-weighted mean size of 2-3 µm. Despite their worldwide clinical utility as a diagnostic contrast agent, and their continued and ongoing success as a local therapeutic vector, the fundamental interplay between microbubbles - including bubble-bubble interaction and the effects of a neighboring viscoelastic vessel wall, remain poorly understood. In this work, we developed a finite element model to study the physics of the complex system of two different-sized bubbles (2 and 3 µm in diameter) confined within a viscoelastic vessel from a resonance response perspective (3-12 MHz). Here, we focus on the effect of micro-vessel wall viscosity on the resulting vibrational activity of the two-bubble system. The larger bubble (3 µm) was not influenced by its smaller companion bubble, and we observed a significant dampening effect across all transmit frequencies when confined within the vessel of increasing viscosity, an expected result. However, the smaller bubble (2 µm) was highly influenced by its larger neighboring bubble, including the induction of a strong low-frequency resonant response - resulting in transmit frequency windows in which its response in a lightly damped vessel far exceeded its vibration amplitude when unconfined. Further, micro-vessel wall dynamics closely mimic the frequency-dependence of the adjacent bubbles. Our findings imply that for a system of multi-bubbles within a viscoelastic vessel, the larger bubble physics dominates the system by inducing the smaller bubble and the vessel wall to follow its vibration - an effect that can be amplified within a lightly damped vessel. These findings have important implications for contrast-enhanced ultrasound imaging and therapeutic applications.