Wimpy virtual instances equipped with small numbers of cores and RAM are popular public and private cloud offerings because of their low cost for hosting applications. The challenge is how to run latency-sensitive applications using such instances, which trade off performance for cost. In this study, we analytically and experimentally show that simultaneously scaling resources at coarse granularity and workloads, i.e., submitting multiple query clones to different servers, at fine granularity can overcome the performance disadvantages of wimpy VM instances and achieve stringent latency targets that are even lower than the average execution times of wimpy servers. To such an end, we first derive a closed-form analysis for the latency under any given VM provisioning and query replication level, considering cloning policies that can (not) terminate outstanding clones with (without) an overhead. Validated on trace-driven simulations, our analysis is able to accurately predict the latency and efficiently search for the optimal number of VMs and clones. Secondly, we develop a dual elastic scaler, DuoScale, that dynamically scales VMs and clones according to the workload dynamics so as to achieve the target latency in a cost-effective manner. The effectiveness of DuoScale lies on the observation that the application performance only scales sub-linearly with increasing vertical or horizontal resource provisioning, i.e., resources per VM or number of VMs. We evaluate DuoScale against VM-only scaling strategies via extensive trace-driven simulations as well as experimental results on a cloud test-bed. Our results show that DuoScale is able to achieve the stringent target latency by using clones on wimpy VMs with cost savings up to 50%, compared to scaling brawny VMs that have better performance at a higher unit cost.