It sounds like you have a 4x6 'top plate' holding the roof, with a separate header over the garage door opening. I'm assuming the cavity between them includes cripples.
The 4x6"x8ft beam alone couldn't carry the weight, but the beam assembly which includes the cripples and door header are likely the reason it fared so well with lifting the welder in the past. It would take a lot more detail and knowledge to be able to say just how much weight the beam could 'actually' lift - plus we'd have to know more about the roof to figure out how much it's already bearing. You can see how this becomes a less-than-simple question.
An easier way would be to measure for deflection at the center of the door opening with a known load. Using that, you could extrapolate a conservative max load that you could hang from the beam before getting into iffy territory.
It sounds like you've already resolved not to use the beam for the 1200lbs lift, which is probably for the best anyway. It's bad enough to drop an engine or item, it's even worse when it takes the house with it!
