In this work we report experimental evidence for the weak high-temperature ferromagnetism in Bi1-x R x FeO3 (R = Dy, Y) compounds by systematic characterizations, excluding the possible side-effects from other iron-based impurities. Remarkable saturated magnetic moment was observed in the Y-substituted samples, Bi1-x Y x FeO3, which is larger than the moment obtained in Bi1-x Dy x FeO3, the Dy-substituted samples with antiferromagnetic background. The physical origin of the weak ferromagnetic transition is discussed and serious lattice distortions have been identified based on the x-ray diffraction and Raman scattering data, although the rhombohedral structure symmetry remains unchanged upon the substitutions. It is believed that the structural distortion suppressed cycloid spin structure is the main factor for the enhanced magnetization in Bi1-x R x FeO3 compounds. Additionally, the Dy3+-Fe3+ antiferromagnetic coupling, which strengthens the antiferromagnetic interaction in Bi1-x Dy x FeO3 compounds, acts as the driving force for the magnetic discrepancy between Bi1-x Y x FeO3 and Bi1-x Dy x FeO3 samples.