Databases as a service (DBaaS) transfer the advantages of cloud computing to data management systems, which is important for the big data era. The allocation in a DBaaS system, i.e., the mapping from databases to nodes of the infrastructure, influences performance, utilization, and costeffectiveness of the system. Modeling databases and the underlying infrastructure as weighted graphs and using graph partitioning and mapping algorithms yields an allocation strategy. However, graph partitioning assumes that individual vertex weights add up (linearly) to partition weights. In reality, performance does usually not scale linearly with the amount of work due to contention on the hardware, on operating system resources, or on DBMS components. To overcome this issue, we propose an allocation strategy based on penalized graph partitioning in this paper. We show how existing algorithms can be modified for graphs with nonlinear partition weights, i.e., vertex weights that do not sum up linearly to partition weights. We experimentally evaluate our allocation strategy in a DBaaS system with 1,000 databases on 32 nodes.