Rear wheel backing plate

I was removing my rear wheel this afternoon to replace the knobbie with a new tw4 bridgstone when I discovered a crack near, and through the lug that slides onto the swing arm which holds the brake in position. A new one is available at $80.00. My question is will welding the plate weaken it or make it stronger. Also I wonder if any other forum members have experienced this brakeage. My supposition is that the previous owner replaced the rear sprocket with a smaller one (45) and did not shorten the chain, leaving the rear wheel too far extended leaving the brake too far extended from the lug on the frame causing extreme leverage on the end if the backing plate. Obviously his error was discovered as the chain is proper length now. Glad I discovered the crack before it broke off completely and perhaps locking up the rear wheel. Suggestions appreciated ------Scotsman