I don't think you can think of it as becoming heavier in the traditional sense, as the higher speed does not increase the force of gravity. There are several (

I don't think you can think of it as becoming heavier in the traditional sense, as the higher speed does not increase the force of gravity. There are several (roughly equivalent) ways to describe what happens as you approach the speed of light. One is that instead of gaining mass, you gain extra inertia, making changing the velocity require more force. This makes it appears to outside observers like your acceleration slows down. I don't particularly like this explanation as it doesn't explain why your rate of energy usage appears to go down (as that is more a function of your clock). I prefer the other explanations: Another is that your clock slows down relative to the outside world so you have less time to apply your force so you need more force to apply the same externally visible acceleration. Another is that the outside world looks shrunk in the direction of travel, so again you have less distance to a apply your force to drive the externally visible acceleration. This is effectively the same as previous since distance=time*speed.