1. A difficult or disagreeable responsibility or necessity; a burden or obligation.
2.3. The burden of proof
a. A stigma.
This according to The Free Dictionary (TFD here onwards). While looking at that, I stumbled upon (not in the Firefox application sense) encumbrance, and then - fardel. TFD gives the following definition:
1. A pack; a bundle.
2. A burden.
Which I thought was quite cool. For reasons unknown, it brings to mind Mexican food and coffee burros, which is possibly appropriate in the burden sense (those poor donkeys). I guess I like the sound of "The burden of proof", and using some creative license and having a decent story behind it: "The Fardel of Proof" (or maybe even: The Burro of Proof). I like it, though I have no idea where I'd use it without having the fardel of sounding overcomplicated and fancy.