Plasmids are one of the most commonly used platforms for genetic engineering and recombinant gene expression in bacteria. The range of available copy numbers for cloning vectors is largely restricted to the handful of Origins of Replication (ORIs) that have been isolated from plasmids found in nature. Here, we introduce two systems that allow for the continuous, finely-tuned control of plasmid copy number between 1 and 800 copies per cell: a plasmid with an anhydrotetracycline-controlled copy number, and a parallelized assay that is used to generate a continuous spectrum of 1194 ColE1-based copy number variants. Using these systems, we investigate the effects of plasmid copy number on cellular growth rates, gene expression, biosynthesis, and genetic circuit performance. We perform single-cell timelapse measurements to characterize plasmid loss, runaway plasmid replication, and quantify the impact of plasmid copy number on the variability of gene expression. Using our assay, we find that each plasmid imposes a 0.063% linear metabolic burden on their hosts, hinting at a simple relationship between metabolic burdens and plasmid DNA synthesis. Our systems enable the precise control of gene expression, and our results highlight the importance of tuning plasmid copy number as a powerful tool for the optimization of synthetic biological systems.