The tooltip showing strengths and weaknesses is a great idea. It should help me figure out why it's not a good idea simply to blob my ships.
However, the relationship between what I'm seeing on the tooltip and what I'm seeing on the screen needs to be a bit stronger, I think. It would be nice if the R key had an additional effect: highlighting enemy ships that the selected ship is strong/weak to. This would mean that the R key would be active outside of just displaying a tooltip, so it would need to be able to function simply on selected ships (so I can select one of my ships or ship types and hold R to see what it should be targeting).
I think that would make the R-tooltip a lot more valuable and useful. Right now, especially with ships that have lots of strengths and weaknesses, the list becomes very unwieldy and hard to scan.
If the above is not possible, then at least this: when you have the R-tooltip active, enemy ships that are in the current system should be highlighted in the tooltip list. That will make longer lists more useful, since I'll at least know what I should be paying attention to at that moment.