Check the rest of the frame for rust and freeze damage, often they need repair around the sidestand bracket weld. I replaced that entire tube on one bike, your repair won't be so bad. If it had been extensively modified there would be more signs of it.
Like John said, the bigger the gap, the more tendency it has to pull. It is rather curious, that should be one of the more ridged parts of the frame you wouldn't expect it to flex much.