When growing wheat, one of the non-chemical methods of weed regulation is to choose wheat varieties which have a high ability to compete with weeds. The first aim of the research was the estimation of the relationships between the morphological features and canopy parameters of six spring wheat varieties. The second aim was the estimation of the varieties’ competitive ability against weeds. The third aim was the estimation of the grain yield of the six varieties. The experiment was carried out in the 2011–2013 time period, on fields which had been organically managed since 1994. Different features affected the weed infestation levels of the spring wheat varieties. For Bombona, negative correlations between the number of weeds and the height, dry matter of wheat, and wheat density, were proved. For Brawura, Hewilla, and Żura, the height, number of tillers, and dry matter of wheat were the main factors influencing weed abundance. A strong negative correlation between the number of weeds and the dry matter of wheat was found for Parabola. Cluster analysis indicated that Bombona and Brawura were the most competitive against weeds, while Monsun and Parabola were characterized as being the least competitive against weeds. Weed number significantly affected the grain yield of spring wheat (r = –0.418). The grain yield was positively correlated with the number of tillers (r = 0.459) and ears (r = 0.355), and the height (r = 0.534) and wheat dry matter (r = 0.411). Bombona and Brawura were the lowest yielding varieties (3.03 and 3.20 t ∙ ha–1, respectively), whereas the highest yield was achieved by Żura (3.82 t ∙ ha–1, on average).