Federal funding for basic scientific research is the cornerstone of societal progress, economy, health and well-being. There is a direct relationship between financial investment in science and a nation's scientific discoveries, making it a priority for governments to distribute public funding appropriately in support of the best science. However, research grant proposal success rate and funding level can be skewed toward certain groups of applicants, and such skew may be driven by systemic bias arising during grant proposal evaluation and scoring. Policies to best redress this problem are not well established. Here, we show that funding success and grant amounts for applications to Canada's Natural Sciences and Engineering Research Council (NSERC) Discovery Grant program (2011-2014) are consistently lower for applicants from small institutions. This pattern persists across applicant experience levels, is consistent among three criteria used to score grant proposals, and therefore is interpreted as representing systemic bias targeting applicants from small institutions. When current funding success rates are projected forward, forecasts reveal that future science funding at small schools in Canada will decline precipitously in the next decade, if skews are left uncorrected. We show that a recently-adopted pilot program to bolster success by lowering standards for select applicants from small institutions will not erase funding skew, nor will several other post-evaluation corrective measures. Rather, to support objective and robust review of grant applications, it is necessary for research councils to address evaluation skew directly, by adopting procedures such as blind review of research proposals and bibliometric assessment of performance. Such measures will be important in restoring confidence in the objectivity and fairness of science funding decisions. Likewise, small institutions can improve their research success by more strongly supporting productive researchers and developing competitive graduate programming opportunities.