I was booked in Basic Economy LAS-JFK on AA 969 yesterday. Before boarding, the gate agent made an announcement that they were looking for 40 volunteers, giving each a $1200 voucher but they couldn't guarantee when people's next flight would be since their only other nonstop that day was also oversold. Obviously pandemonium ensued. The gate agent then said that because it was a weight restriction due to weather, normal compensation rules wouldn't apply. At some point they said 7 people without carry-on's could board so I jumped at the opportunity given the complete chaos at the gate. We left the gate only to return, again due to weight, and they got 13 more volunteers off the plane. When I was at the gate, there were 2 agents only one of whom was working on rebooking pax. Because I booked Basic Economy, I was worried I would get last priority and be stuck there for days. If I would have not boarded to begin with, would I have been eligible for the full 400% compensation for IDB? Was the agent completely full of it blaming the issue on 'weather'?