This is a great question!
so can you lift 200% of body weight in 0.5 gravity and only 50% body weight in 2 gravity?
When we interact with objects having significant, large mass on Earth, there are two ways that we experience the mass; weight and inertia.
Gravitational mass (as weight)
This is the one that you discuss in your question, and your understanding seems to be correct. Let's say you can easily and comfortably lift a 50 lb. bag of something from the ground and carry it from point A to point B and set it down. Then if you are living in a lunar base on the Moon you could potentially lift a 300 lb. bag of something off of the ground as well.
You would have the strength to
- get it off of the floor
- accept it if someone slowly and carefully passes it to you at a comfortable hight
However if you weren't careful, you might hurt yourself badly or damage something trying to lift it and carry it from point A to point B.
This is because while an objects weight scales with the strength of local gravity, its inertial mass doesn't change.
Imagine that you have a Plymouth Satellite station wagon, and you've run out of gas and stopped in an awkward place (not that this has ever happened to me, and not that it hasn't either). If you make sure it is in neutral and the tires are properly inflated and the brakes aren't stuck, you can push on it horizontally and it will slowly start moving.
If you are smart (which I wasn't) you will think about what you are going to do when you want it to stop ahead of time because you'll realize (which I didn't) that while the weight is a non-issue, the inertia is really important. Even though you are not lifting it, you need to be very careful once it is in motion because you will need to slow it down and stop it as well!
So to lift your 300 lb. bag, you'll need to pull on it to get it moving up, but your lifting will be like in slow motion. And if you pull too long, it may be moving too fast to slow down once it passes your waist on its way to your shoulders, and when you try to get it to stop at shoulder height, you may use muscles that you haven't before, and you may discover that since the bag weighs far more than you do, your feet leave the ground!
Then it will slow down, reverse direction, and hopefully you have your shoulder under it and your legs bent in order to bring the 300 lbs. to a stop at a comfortable height.
So you will need to train how to safely manage masses much larger than yourself that weigh less than you did back on Earth!
Source: Find Classic Cars' 1973 plymouth satellite wagon, rare, survivor