Rooted - built up (ἐῤῥιζωμένοι - ἐποικοδομούμενοι)
Note the change of metaphor from the solidity of military array to walking, rooting of a tree, and then to building. The metaphors of rooting and being founded occur together, Eph 3:17. Compare 1Co 3:9. In Jer 1:10, ἐκριζοῦν to root out is applied to a kingdom, and the words to build and to plant follow. It must be said that ῥιζόω to cause to take root is often used in the sense of firmness or fixedness without regard to its primary meaning. Built up. The preposition ἐπί upon indicates the placing of one layer upon another. See on Act 20:32, and see on 1Co 3:9. Compare 1Co 3:10-14; Eph 2:20. note also the change of tenses: having been rooted (perfect participle), being (in process of) built up and strengthened (present participle).
In Him (ἐν αὐτῶ)
Rather than upon Him, as might have been expected. In this and in the Ephesian epistle, Christ is represented as the sphere within which the building goes on. Compare Eph 2:20. The whole upbuilding of the Church proceeds within the compass of Christ's personality, life, and power.
For Paul's emphasis on thanksgiving, see Rom 1:21; Rom 14:6; 2Co 1:11; 2Co 4:15; 2Co 9:11, 2Co 9:12; Eph 5:20; 1Ti 2:1, etc. Εὐχαριστός thankful, εὐχαριστεῖν to give thanks, εὐχαριστία thanksgiving, are found only in Paul's writings.