This case is too/fairly heavy, but I can still lift it. Which is better, ‘too’ or ‘fairly’ ?
If it is too heavy for some other constraint, you need to specify, unless it is clear from previous context:
This case is too heavy for that shelf (I can put it up, but the shelf will break if I do)
This case is too heavy for my mother to lift (but I am stronger)
This case is too heavy to carry for a long distance (but I can lift it briefly)
Otherwise, too heavy for me to lift is the only reasonably implied meaning, and that’s obviously impossible.