Weil structures her entire worldview around two opposing forces: gravity (pesanteur) and grace (grâce). The analogy is physical but deeply philosophical.
Gravity, in the physical world, pulls everything downward, toward entropy, toward the lowest energy state, toward dissolution. Weil uses it as a metaphor for the natural movement of the human soul without grace: toward self-interest, self-protection, resentment, the need to dominate, the compulsion to fill the void with distraction. We resent insults and want revenge, that is gravity. We feel sad and reach for consolation, that is gravity. We suffer and want to pass the suffering on to someone else, that is gravity. Gravity is not evil; it is simply the default trajectory of a self left to its own devices.
Grace, grâce, is the force that moves against gravity: the possibility of responding to an insult without resentment, of receiving suffering without passing it on, of facing the void without filling it. Grace is not achieved by willpower (that would just be gravity in a different form, ego forcing its will over its inclinations). It can only be received, and received only by the soul that has sufficiently emptied itself through attention and decreation.
Weil's God is strikingly absent in ways that distinguish her from mainstream Christian mysticism. God, she says, withdrew from creation to allow creation to exist, a concept borrowed from the Kabbalistic idea of tzimtzum (divine contraction). God is present in the world precisely through this absence, through the void, through affliction, through the places where all consolation has failed. Christ on the cross, crying "My God, my God, why have you forsaken me?", is, for Weil, the paradigmatic instance of the void: the point of maximum affliction, maximum abandonment, and therefore the point of maximum contact with the hidden God.
Weil never converted to Catholicism despite deep attraction to it, she refused baptism, in part because she felt called to remain on the threshold, in solidarity with those outside the church who could not find their way in. This threshold position shapes her philosophy: she is always attending to what is excluded, what suffers, what is overlooked. Her political writing on colonialism, on factory labor, and on rootlessness (The Need for Roots, 1943) applies the same attentiveness to social and political reality that her mystical writing applies to the soul.
For secular readers, the most valuable dimension of Weil may be her account of attention as an ethical practice: the cultivation of the capacity to truly see the other, to receive their reality without filtering it through your own needs and agendas. This requires nothing theological to be taken seriously. It is a rigorous phenomenological and ethical claim about what genuine human contact requires, and why it is so rare and so difficult.