I've read a little bit about shoes for running on asphalt and for trail-running, but they always refer to lightweight people. I would like to know what to look for in a running shoe when my weight is between 80 and 85 kilograms?
The best thing you could probably do would be to find a dedicated runner's shop. We've got one where I live and they are really specializing in running shoes.
A good runner's shop should be able to do several things for you:
It might be hard to find a shop like that, but it's really worth it once you do.