Rats do not go for weepers, actually, because they are already too much infected. You won't ever have to hide Weepers bodies, which is cool, actually. Well just don't leave them where they can be found during the mission, raising the alarms. I also wonder if, when found by guards, they won't count as a kill for you. Anyway, don't fear the rats for the Weepers!
Just be sure they didn't clip through the floor when you darted them. Happened to me, and one of them drowned after his head ( just his head ) fell tthrough the floor and right in the water. I had only sleep-darted him where he was standing.