^ That was a joke right? NOBODY CAN BE AN AGENT OF ORDER UNDER THOSE CIRCUMSTANCES. Her restrictions on freedom of expression, compared with liberty being also a vital need of the soul meant that order could never be achieved, since the liberty becomes so restrictive that it cannot be considered liberty at all!
Whilst her conceptions before the listing of the needs of the soul are rather intriguing, she absolutely butchers it in the way she suggests it to be implemented in the Needs of the Soul! Not to mention the unsupported premises in her arguments!
Yes, that is why there is so much hate 
Haha I agree that some of her claims are a bit 'out there', but the crux of her argument is solid. Weil was put into the course because none of the other philosophy even considered what is loosely referred to as the 'universal conscience'. When we see a baby getting murdered, we don't just nod and say 'oh, that's bad'; we feel something inside of us. In the Need for Roots (lol), Weil probes this seemingly inexplicable sensation, and, while her explanation for why this sensation exists might not appeal to everyone, especially those who have an aversion to all things religious, I think that she has much to offer. Her articulation of the needs of the soul, however, leaves much to be desired; I agree on that head.
I think Weil tends to get shat on a bit more than is warranted, but come on, she was pretty lousy to study. Everything was either utterly abstracted from reality (the eternal realm of the soul) and difficult to apply to everyday life, or painfully obvious but entirely and annoyingly unjustified. (The obligation to help others in need if you have the means to do so is universal. Why? Do you disagree? No? Then nobody disagrees and it must be true. You do? Then you're mentally unwell and distinct from society at large and it's still true.)
I'm not sure what exactly you mean by 'abstracted from reality', but I don't see what further justification she needs. Of course, if you take what she wrote literally, then some of claims might seem completely nonsensical. But I don't think she actually believed that there was a realm situated geographically above the physical realm, or the 'realm of facts' as she puts it, in which random 'obligations' floated around. The language she uses is, I agree, a bit odd, and she could have chosen other, less controversial, less religious terms to communicate her sentiments. As I said earlier, what she is trying to articulate is this thing which many people refer to as the 'conscience'. She doesn't actually use the word conscience as far I'm aware. She uses the term 'eternal destiny' or something, which may sound a little off-putting, but I don't think that she should be written off simply on account of her diction.
And just with regard to the last bit of your post, of course, no philosopher can possibly know what is the case for every single human being in existence. She is simply hypothesizing, or rather generalizing her own personal experiences. I think that every time we articulate a belief, such as 'murder is bad', we are doing just this. "Of course, everyone believes murder is bad. If you don't believe this, you are mentally disturbed in some way or other, and should be removed from society..."
Anyway, I feel I have derailed the topic. Although since this is the 'Countdown Thread', perhaps anything is appropriate...
EDIT: I'd just like to add, yes gosh, she was annoying to study!! Especially the 20 or so pages in which she systematically lists what she feels are the most important needs...