Jamieson, Fausset and Brown on 2 Samuel 1:13-15

13-15. David said unto the young man ... Whence art thou?--The man had at the outset stated who he was. But the question was now formally and judicially put. The punishment inflicted on the Amalekite may seem too severe, but the respect paid to kings in the West must not be regarded as the standard for that which the East may think due to royal station. David's reverence for Saul, as the Lord's anointed, was in his mind a principle on which he had faithfully acted on several occasions of great temptation. In present circumstances it was especially important that his principle should be publicly known; and to free himself from the imputation of being in any way accessory to the execrable crime of regicide was the part of a righteous judge, no less than of a good politician.

2Sa 1:17-27. David Laments Saul and Jonathan.