Approvingly

adv. [f. prec. + -LY².] In an approving manner; so as to imply approval.

1837.  Carlyle, Fr. Rev., V. ii. II. 285. His two brothers … who look down on him approvingly.

1882.  J. Hawthorne, Fortune’s Fool, I. xii. Nodding her head approvingly.