Bobbin tool friction stir welding (BTFSW) is a variant of the FSW process which uses the special two-shoulder tool that forms the top and bottom of a weld surface. As such, a significant simplification of the welding setup is achieved. One of the dominant parameters of the BTFSW process is the interference between the tool shoulder pinch gap and the weld metal thickness. In this research, the influence of interference of the square pin tool with convex shoulders on process temperature, microstructure, tensile, impact, and bend performance were studied, and appropriate correlations were devised. The base metal was an aluminum–magnesium alloy in which the interference varied in the range of 0.1 to 0.5 mm. Wormhole defects and irregularities were found in all specimens except in the specimen welded with 0.4 mm interference. An optimal interference of 0.4 mm resulted in the best mechanical properties, which, in terms of tensile strength and reduction of area, were similar to the base metal. Furthermore, the impact strength was significantly higher, which was attributed to the grain refinement effect in the nugget zone.