IMS we would say "it is a game about magic". Such a situation as presented would be allowed to be solved by any of the proposed methods so far without problems. If we want to nitpick, we can always do that, but it is hardly any fun for us to do it.
Manipulate, not support a person climbing it. So, if you can manipulate the rope around something and tie it off, sure, no problem. But someone isn't going to be able to climb up that rope, since the spell has no strength above and beyond what it takes to manipulate the rope.
No, I'm talking about force. I may have been unclear. I was referring to this effect: the magus holds an end of the rope at a certain point in space, says "Nailed!", and that end of the rope is then affixed at that point. No matter how hard one pulls on the rest of the rope, that extremity will be nailed at the spot (pulling hard enough may break the rope, of course). Note that this does not tie the (extremity of the) rope to an object, it ties it to that "position", and it's a classic trope of many fairy tales both old and modern. In our saga, this effect is achieved using the guideline "Manipulate an object etc.", in this case the rope. I am under the impression that neither you nor jonathan.link think it's within the (admittedly somewhat vague) guideline - but if that's the case, under which guideline would you allow it?
Already answered that one I'd thought
Basically, I'd expect base ReAn to be able carry about the mass of a Size +1 animal - a pony to wit.
The fact that you are carrying a Herbam entity (the cart) or a Corpus entity (grogs) or even Terram entities (weapons and armour) should make things harder, not easier.
So yeah, if you're going to be lifting that much on a single rope, prepare to toss in a few magnitudes for "lotsa powar"
Note that there's a fundamental difference between lifting, and holding up something that's already up (in modern physics terms, the latter involves no work). Lifting a mountain requires a pretty high level spell. It's canonical that a level 20 spell allows a grog to hold up a mountain that's tossed onto him (assuming the mountain does not crumble under the stress). In the case of this thread, all you need is to hold up the stuff as you move it across the river. However, I think that this issue is one that deserves its own thread and should not hijack this one. Let me start one!