More separates Lovecraft from Simone Weil than unites them. Still, the description below of Weil's appeal shares something with Lovecraft's appeal and place.
THE culture-heroes of our liberal bourgeois civilization are anti-liberal and anti-bourgeois; they are writers who are repetitive, obsessive, and impolite, who impress by force—not simply by their tone of personal authority and by their intellectual ardor, but by the sense of acute personal and intellectual extremity. The bigots, the hysterics, the destroyers of the self—these are the writers who bear witness to the fearful polite time in which we live. Mostly it is a matter of tone: it is hardly possible to give credence to ideas uttered in the impersonal tones of sanity. There are certain eras which are too complex, too deafened by contradictory historical and intellectual experiences, to hear the voice of sanity. Sanity becomes compromise, evasion, a lie. Ours is an age which consciously pursues health, and yet only believes in the reality of sickness. The truths we respect are those born of affliction. We measure truth in terms of the cost to the writer in suffering—rather than by the standard of an objective truth to which a writer's words correspond. Each of our truths must have a martyr.
....such writers as Kierkegaard, Nietzsche, Dostoevsky, Kafka, Baudelaire, Rimbaud, Genet—and Simone Weil—have their authority with us precisely because of their air of unhealthiness. Their unhealthiness is their soundness, and is what carries conviction.
....Perhaps there are certain ages which do not need truth as much as they need a deepening of the sense of reality, a widening of the imagination. I, for one, do not doubt that the sane view of the world is the true one. But is that what is always wanted, truth? The need for truth is not constant; no more than is the need for repose. An idea which is a distortion may have a greater intellectual thrust than the truth; it may better serve the needs of the spirit, which vary. The truth is balance, but the opposite of truth, which is unbalance, may not be a lie.
....We read writers of such scathing originality for their personal authority, for the example of their seriousness, for their manifest willingness to sacrifice themselves for their truths, and—only piecemeal—for their "views." As the corrupt Alcibiades followed Socrates, unable and unwilling to change his own life, but moved, enriched, and full of love, so the sensitive modern reader pays his respect to a level of spiritual reality which is not, could not, be his own.
....Some lives are exemplary, others not; and of exemplary lives, there are those which invite us to imitate them, and those which we regard from a distance with a mixture of revulsion, pity, and reverence. It is, roughly, the difference between the hero and the saint...
From the essay "Simone Weil" by Susan Sontag (1963), collected in: AGAINST INTERPRETATION