How to set arbitrary sort order of nodes per view

I have several views on a site, each view filtering nodes by one specific term. Some nodes appear in more than one view. What I need is a way to set an arbitrary sort order - like a weight - in which each node appears, per view, e.g.:

Node A has terms "News" and "Projects". It should be listed on position 4 in the "News" view and on position 2 in the "Projects" view.

If each node were appearing in one view only then such an arbitrary sort order could be achieved simply with a weight field. Here, however, some kind of relationship between node, term and sort order is needed...

Any ideas? (The Relation module? How would this be done?)