A few notes

“The Septuagint and Vulgate treat this as two psalms, the second of them beginning at verse 10 (but some Heb. MSS make a similar break after verse 11).” Kidner, 407. 

“He has come now to the temple to tell the whole assembly what has happened, and to offer God what he had vowed to Him in his extremity” Kidner, 407. 

“The situation was one of deadly threat (3, 8, 15), brought about by human deceitfulness (11) and personal lack of discernment (6)” Motyer, 563. “Either the psalmist has been delivered from what appeared to be a fatal illness (vss. 2, 8) or from false accusers (vss. 10-11) who plotted his death. Out of gratitude for his deliverance, he thanks God publicly so that others may share in his joy and faith” Miller, 378. The Psalm is “far from wallowing in personal details, (and) focus(es) attention on what God has done” Laymen, 683.  

“Such psalms as this, once written down, would help many another person to find words for his own public thanksgiving” Kidner, 407. 

116:15 Precious in the sight of the LORD- “Precious could mean either ‘highly valued’ or, in a less happy sense, ‘costly’” Kidner, 410. “Precious here means costly (cf. Ps. 72:14; I Kings 5:17; 7:9-11)” Miller, 380. II Kings 1:13-14; Prov. 20:15. 

Is the death of His godly ones- “The death of the devout costs Yahweh dear” (cf. Mt. 10:29-31; and in ultimate terms, Jn. 10:28f.)” Kidner, 411. “The death of a saint is not something the LORD considers as cheap” BK, 877. 

 “Verse 15 has puzzled commentators for millennia. Most versions follow closely the translation of the 1611 Authorized Version: ‘Precious in the sight of the LORD is the death of His saints.’” NICOT, 861. What does this verse mean? “The death of his saints, ‘his beloved,’ is like a precious jewel which he bestows- precious to him and them because at death he receives them home. In this sense, death is the final and greatest earthy blessing of God on His people” Motyer, 564. Phil. 1:20-23; Rev. 14:13.

On the other hand, this passage can be understood another way. The NET translation has “The LORD values the lives of his faithful followers.” “The word usually translated as ‘precious’ is from the Hebrew root yaqar, which means ‘be dignified, honorable, heavy, valuable.’ It occurs nine times in the book of Psalms (36:7; 37:20; 45:9; 49:8, 12, 20; 72:14; 116:15; 139:17)” NICOT, 861. “He has learned by experience that the premature death of God’s people ‘costs Yahweh dear’ (JB; cf. 72:14) and that He is quick to avert such a tragedy” Laymen, 684. “As translated by the NIV, verse 15 seems strange and out of context, appearing to say that God delights in the death of His faithful servants....The psalmist is one of God’s faithful servants, and God had just saved him from death” Longman, 397. “The NIV and the NRSV make v. 15 sound as if God welcomes the death of the faithful, but the whole point of the psalm is that God will life and works to make life a reality” McCann, 1149. God “does not lightly permit adversity (‘death’’ vs. 3, 8) or an early death (cf. 79:11; 102:20). They are ‘precious’ (cf. 72:14) to Him” VanGemeren, 728. On the same page, VanGemeren, 728, refers to a study by John A. Emerton “The death of His beloved creates sadness to our Lord.” “The psalmist has learned by experience how reluctant Yahweh is to allow the premature death of those united to Him in a covenant relationship, and how quickly He rushes to avert such a tragedy (cf. Ps. 72:14)” Allen, 115.