What is the basis from the Church's Sacred Deposit of the Faith for the concept of "gradualism"?

In Familiaris Consortio, (Latin roughly translated as "of family partnership"¹, but titled in English On the role of the Christian Family in the Modern World), a postsynodal Apostolic Exhortation written by Pope St. John Paul II [the Great] and given on November 22, 1981, it appears that the saintly Pope set out clarify what is 'the law of gradualness' and contrast it with 'gradualness of the law,'

"And so what is known as 'the law of gradualness' or step-by-step advance cannot be identified with 'gradualness of the law,' as if there were different degrees or forms of precept in God's law for different individuals and situations [...]".²

^{1. cf. Familiaris Consortio | Wikipedia. Online Latin to English has "family-company".}

^{2. John Paul II, Homily at the Close of the Sixth Synod of Bishops (Oct. 25, 1980), 8: AAS 72 (1980), 1083.}

This article - St. John Paul II and "the law of gradualness" by Province of St. Joseph | Dominican Friars - using an excerpt from a Zenit article by Fr. Dominic Legge, O.P., explains “the law of gradualness”

What John Paul called “the law of gradualness” does not refer to a “gradual” turning away from sin, but to the perennial Christian doctrine that we are not yet perfect in the first moment of our conversion. When we receive a grace of conversion, we break definitively from evil and then gradually advance in holiness. We may even fall back into grave sin, but, helped by grace, we repent and start anew. Here, the sacrament of Penance has an important role to play: it calls us to renounce our sins definitively with a firm purpose of amendment. In effect, he who will not yet repent, will not yet accept God’s mercy, and so is not forgiven. (CCC no. 1451; DH 1676³.)

The Zenit article continues

As St. John Paul says, the “law of gradualness” presupposes this turning-away from evil, so that one can begin to walk “step-by-step” on the upward – that is, gradually ascending – path of good. “What is needed is a continuous, permanent conversion which, while requiring an interior detachment from every evil and an adherence to good in its fullness, is brought about concretely in steps which lead us ever forward.” (Familiaris Consortio no. 9.) The ascent is gradual, but the renunciation of sin cannot be.

The law understood this way, is in harmony with Scripture

Mark 1:14-15 (RSVCE) 14 [...] Jesus came into Galilee, preaching the gospel of God, 15 and saying, “The time is fulfilled, and the kingdom of God is at hand; repent, and believe in the gospel.”

Acts 2:38 (RSVCE) 38 And Peter said to them, “Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit.

First step is always, "break with sin", and then step-by-step advancement to the perfection that all have been called to.

^{3. cf. Sources of Catholic Dogma by Denzinger, Chap. 4. Contrition | Council of Trent, Session 14, the Decree regarding the Sacraments of Penance and Extreme Unction [Anointing of the Sick].
897 Contrition, which has the first place among the aforementioned acts of the penitent, is a sorrow of the soul and a detestation of sin committed, with a determination of not sinning in the future. This feeling of contrition is, moreover, necessary at all times to obtain the forgiveness of sins, and thus for a person who has fallen after baptism it especially prepares for the remission of sins, if it is united with trust in divine mercy and with the desire of performing the other things required to receive this sacrament correctly. The holy Synod, therefore, declares that this contrition includes not only cessation from sin and a resolution and a beginning of a new life, but also hatred of the old, according to this statement: "Cast away from you all your transgressions, by which you have transgressed, and make to yourselves a new heart and a new spirit" [Ezech. 18:31 ]. And certainly, he who has considered those lamentations of the saints: "To Thee only have I sinned, and have done evil before Thee" Ps. 50:6]; "I have labored in my groanings; I shall wash my bed every night" Ps. 6:7]; "I will recount to Thee all my years in the bitterness of my soul" [Isa. 38:15], and others of this kind, will readily understand that they emanate from a certain vehement hatred of past life and from a profound detestation of sins.}

Looking at the point below from the 2014 Synod's "Relatio post disceptationem", one can see why His Eminence Cardinal Raymond Leo Burke says, '[it] invokes repeatedly and in a confused manner principles which are not defined, for example, the law of graduality.'

13 From the moment that the order of creation is determined by orientation towards Christ, it becomes necessary to distinguish without separating the various levels through which God communicates the grace of the covenant to humanity. Through the law of gradualness (cf. Familiaris Consortio, 34), typical of divine pedagogy, this means interpreting the nuptial covenant in terms of continuity and novelty, in the order of creation and in that of redemption.

From the Reports of Circuli Minores, Circulus Anglicus "A" responded

We had serious questions about the presentation of the principle of GRADUALITY. We wished to show in our amendments that we are not speaking of the GRADUALITY of DOCTRINE of faith and morals, but rather the gradual moral growth of the individual in his or her actions. - Relatio (Synod 2014) - Circulus Anglicus "A" | Moderator: Em.mo Card. Raymond Leo BURKE | Relator: S.E. Mons. John Atcherley DEW

Please see also:

• Rock of Ages By David Warren, Friday, 17 October 2014 | The Catholic Thing.