The phrase affectionately desirous
(or: out of deep affection) alludes to the profound love and longing that the nurse-mother feels for her child, and indicates that Paul was similarly moved by his love for the Thessalonian believers. The Greek word behind this translation is very unusual, but there is general agreement that it refers to a yearning affection.
1,2,3
8 So, being affectionately desirous of you, we were ready to share with you not only the gospel of God but also our own selves, because you had become very dear to us.