Acinetobacter baumannii is a nosocomial pathogen often associated with multidrug resistance (MDR) infections. Fluoroquinolone resistance (FQR) due to drug target site mutations and elevated expression of RND drug transporters is common among clinical isolates. We describe here a CRISPRi platform that identifies hypomorphic mutations that preferentially altered drug sensitivity in RND pump overproducers. An sgRNA library against essential genes of A. baumannii was constructed with single and double nucleotide mutations that produced titratable knockdown efficiencies and introduced into multiple strain backgrounds. Other than nusG depletions, there were few candidates in the absence of drug treatment that showed lowered fitness specifically in strains overexpressing clinically relevant RND efflux pumps AdeAB, AdeIJK, or AdeFGH. In the presence of ciprofloxacin, the hypomorphs causing hypersensitivity were predicted to result in outer membrane dysfunction, to which the AdeFGH overproducer appeared particularly sensitive. Depletions of either the outer membrane assembly BAM complex, LOS biogenesis proteins, or Lpt proteins involved in LOS transport to the outer membrane caused drug hypersensitivity in at least two of the three pump overproducers. On the other hand, depletions of translation-associated proteins, as well as components of the proton-pumping ATP synthase pump resulted in fitness benefits for at least two pump-overproducing strains in the presence of the drug. Therefore, pump overproduction exacerbated stress caused by defective outer membrane integrity, while the efficacy of drug resistance in efflux overproducers was enhanced by slowed translation or defects in ATP synthesis linked to the control of proton movement across the bacterial membrane.