Multi-tenancy in resource-constrained environments is a key challenge in Edge computing. In this paper, we develop ‘DYVERSE: DYnamic VERtical Scaling in Edge’ environments, which is the first light-weight and dynamic vertical scaling mechanism for managing resources allocated to applications for facilitating multi-tenancy in Edge environments. To enable dynamic vertical scaling, one static and three dynamic priority management approaches that are workload-aware, community-aware and system-aware, respectively are proposed. This research advocates that dynamic vertical scaling and priority management approaches reduce Service Level Objective (SLO) violation rates. An online-game and a face detection workload in a Cloud-Edge test-bed are used to validate the research. The merit of DYVERSE is that there is only a sub-second overhead per Edge server when 32 Edge servers are deployed on a single Edge node. When compared to executing applications on the Edge servers without dynamic vertical scaling, static priorities and dynamic priorities reduce SLO violation rates of requests by up to 4% and 12% for the online game, respectively, and in both cases 6% for the face detection workload. Moreover, for both workloads, the system-aware dynamic vertical scaling method effectively reduces the latency of non-violated requests, when compared to other methods.