As my original email said, the flight was oversold, the gate agent said so.

In the email response I received from UA customer service, they said they don't owe me any compensation b/c of this garbage: "... due to safety-related weight/balance restrictions that limit payload on aircrafts with 60 or
fewer seats,.."

I wonder how overweight issue would be a possibility even before boarding?

In any event, the question is does it give them (UA) the latitude to apply the
'60 or fewer seats rule' after the effect, i.e. overbooking is the primary cause, but tell the customers (the secondary cause) '60 or fewer seats rule' because the rule is/will likely kick in once 60 passengers and baggages are loaded?

I am not sure if the flight left with full head count or less than its passenger capacity, but my hunch is it left with the full passenger load. Is there a place to find this information?

I did read, earlier, the recent article on Delta and United being fined for compensation/codeshare issues. I will wait before complaining to DOT.