The Greek text (to the left) very clearly indicates that the word “gives” does not appear in the Greek text and has been added by the NWT (to the right).

Albert Barnes states:

The language here is cumulative, and is full of meaning and richness.

(1) they were to be “full of God.” That is, he would dwell in them.

(2) they were to be filled with “the fulness of God” - τὸ πλήρωμα τοῦ Θεοῦ  to plērōma tou Theou. On the word rendered “fulness,” see on Eph_1:10, note, 23, note. It is a favorite word with Paul. Thus, he speaks of the “fulness” of the Gentiles, Rom_11:25; the “fulness” of time, Gal_4:4; the fulness of him that filleth all in all, Eph_1:23; the “fulness” of Christ, Eph_4:13; the “fulness” of the Godhead in Christ, Col_1:19; Col_2:9. It means here, “that you may have the richest measures of divine consolation and of the divine presence; that you may partake of the entire enjoyment of God in the most ample measure in which he bestows his favors on his people.”

(3) it was to be with “all” the fulness of God; not with partial and stinted measures of his gracious presence, but with “all” which he ever bestows. (emphasis mine)[1]

Does God’s fullness give? Certainly. God’s fullness imparts peace, joy, and a great many spiritual blessings upon us and in us, but as Albert Barnes indicates, it is not merely what God’s fullness gives, but that God himself dwells in us.  The NWT addition of “gives” to Ephesians 3:19 dilutes the power of Paul’s message, unnecessarily limits God’s fullness to only those gifts he imparts to us and thereby denies God’s presence within us.

The addition of "gives" is not warranted by the Greek text and I feel is completely unnecessary as well as subtly misleading.