BaFe$_2$S$_3$ is a quasi-one-dimensional antiferromagnetic insulator that becomes superconducting under hydrostatic pressure. The magnetic ordering temperature, $T_N$, as well as the presence of superconductivity have been found to be sample dependent. It has been argued that the Fe content may play a decisive role, with the use of 5%mol excess Fe being reportedly required during the synthesis to optimize the magnetic ordering temperature and the superconducting properties. However, it is yet unclear whether an Fe off-stoichiometry is actually present in the samples, and how it affects the structural, magnetic and transport properties. Here, we present a systematic study of compositional, structural and physical properties of BaFe$_{2+delta}$S$_3$ as a function of the nominal Fe excess $delta$. As $delta$ increases, we observe the presence of an increasing fraction of secondary phases but no systematic change in the composition or crystal structure of the main phase. Magnetic susceptibility curves are influenced by the presence of magnetic secondary phases. The previously reported maximum of $T_N$ at $delta$=0.1 was not confirmed. Samples with nominal $delta$=0 present the lowest $T_N$ and the resistivity anomaly at the highest temperature $T^*$ while, for $delta geq 0.05$, both quantities and the transport gap are seemingly $delta$-independent. Finally, we show that crystals free of ferromagnetic spurious phases can be obtained by remelting samples with nominal $delta$=0.05 in a Bridgman process.
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