What is this (727 extension housing)?

If you decide to keep that weight, make darn sure it clears everything- I have had slip yokes that would contact the weight when the suspension compresses, resulting in a "mystery vibration" that would come and go...
Disconnect the driveshaft, put the trans in neutral, and push the slip yoke all the way into the tailshaft. Now turn it- sometimes you can feel the yoke touch the weight as it spins, or even see witness marks on the weight and or yoke. If you do, clearance grind the weight (NOT THE YOKE), or just remove the weight entirely.