Growth habit is an important determinant of competitive ability in legume crops. Erect ‘Iron-Clay’ (IC), semi-erect ‘IT89KD-288’ (288), and prostrate ‘UCR 779’ (779) cowpea genotypes were planted with four densities of common sunflower or common purslane to determine which cowpea growth habit is more competitive to these weeds having markedly different statures. Both sunflower and purslane reduced cowpea relative growth rate (RGR) but at different phases of the growing season. Low-growing purslane had an effect in the earlier part of the season, and sunflower decreased cowpea RGR in the middle of growing season. RGR of genotype IC was the least affected and genotype 779 the most reduced by sunflower. Cowpea apparently compensated for early season purslane competition by increasing RGR after purslane flowering, with RGR for the IC genotype increasing the most and 779 increasing the least. All cowpea genotypes caused a similar reduction in sunflower biomass accumulation; but purslane biomass was most reduced by genotype IC and least affected by genotype 288. Erect genotype IC is more competitive due to its taller stature, greater height growth rate, and higher position of maximal leaf area density, despite a lower photosynthetic rate and light use efficiency than the other cowpea genotypes. Our results suggest that erect cowpea growth habit may be generally more competitive with weeds compared to semi-erect or prostrate growth habit.