Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
The present chapter contains two facts not found in Sa1 31:1-13 - the fastening of Saul's head in the temple of Dagon Ch1 10:10, and the burial of his bones, and those of his sons, under an oak Ch1 10:12. Otherwise the narrative differs from Sa1 31:1-13 only by being abbreviated (see especially Ch1 10:6-7, Ch1 10:11-12), and by having some moral reflections attached to it Ch1 10:13-14.
All his house died together - Not the whole of his family, nor even "all his sons" (see Sa2 2:8-15; Sa2 3:6-15; Sa2 4:1-12). The phrase is perhaps an abbreviation of the expression in the parallel passage of Samuel Sa1 31:6.
For his transgression - Compare Ch1 9:1. The "transgression" intended is probably the disobedience with respect to Amalek, recorded in Sa1 15:1-9 (compare Sa1 28:17-18).