We must distinguish (writes that most accessible of all Puritans, Thomas Watson) between weakness of faith and no faith:-

A weak faith is true. The bruised reed is but weak, yet it is such as Christ will not break. Though thy faith be weak, be not discouraged.

(1.) A weak faith may receive a strong Christ. A weak hand can tie the knot in marriage as well as a strong one; and a weak eye might have seen the brazen serpent. The woman in the gospel did but touch Christ’s garment, and received virtue from him. It was the touch of faith.

(2.) The promise is not made to strong faith, but to true. The promise says not whosoever has a giant-faith, that can remove mountains, that can stop the mouths of lions, shall be saved; but whosoever believes, be his faith ever so small. Though Christ sometimes chides a weak faith, yet that it may not be discouraged, he makes it a promise. Beati qui esuriunt. Matt 5:3.

(3.) A weak faith may be fruitful. Weakest things multiply most; the vine is a weak plant, but it is fruitful. Weak Christians may have strong affections. How strong is the first love, which is after the first planting of faith!

(4.) Weak faith may be growing. Seeds spring up by degrees; first the blade, then the ear, then the full corn in the ear. Therefore, be not discouraged. God who would have us receive them that are weak in faith, will not himself refuse them. Rom 14:1: A weak believer is a member of Christ; and though Christ will cut off rotten members from his body, he will not cut off weak members.’