Because I can't seem to find it, and it moves every route, the only thing I can think of is going to a city, and then moving back and forth between the city and the route, until Latias appears on that Route. Any other suggestions?
The best strategy to catch a Roaming Pokemon is
Find 2 routes that border each other, (or a route that has a building in it,) that can support a Roaming Legendary appearing. I am more unfamiliar with Hoenn then any other region, so you will have to find this yourself.
Get a fast Pokemon with Mean Look, or a Wobbuffet with Shadow Tag. Gengar/Haunter is probably fast enough if you get it to a high enough level. The Shadow Tag Wobbuffet is probably the best idea. It should be noted Arena Trap doesn't work on Levitate.
Start the hunt by going in between routes and checking Latios' location in the Pokedex. If it is not on the route, rinse and repeat. You should know how to do this.
Once you have encountered Latios, you can try catching it in a couple different ways. You said you have weakened it, so if you have a Shadow Tag Wobbuffet or anything similar, you can sit there and throw Ultra Balls, and eventually Timer Balls. If you don't/can't want to do that, just throw Quick Balls, as everytime a Roamer is encountered, a Quick Ball regains it's effectiveness.
Could also just use Master Ball. I hope this is helpful.