The expression is cryptic in Hebrew: Their fat they close.
The term for fat
(חֵלֶב) seems to signify their calloused, insensitive hearts (see also Psalm 73:7; Psalm 119:70). There is even a proposed emendation of the Hebrew to capture this: They close off the fat of their hearts [חֵלֶב לִבָּמוֹ],
that is, their hearts are calloused or indifferent to the people they hurt. This reading assumes haplography, where the ancient scribe accidentally omitted repeated letters in the Hebrew original—in this case, the לב combination. The ESV’s They close their hearts to pity
is an interpretation that basically follows the proposed emendation. It is an acceptable interpretation, yet it does not favour the received Hebrew text, which is problematic since that text is well-attested. Priority needs to be given as much as possible to that text.
The image of fat
is often associated with prosperity and success (Deuteronomy 32:15). In this text, the term applies to the wicked, and as such, it may be depicting them as the prosperous in the world, or their strong rebellion against the Lord (see also Isaiah 6:10). In their prosperity and rebellion against God, they were also calloused toward others.1
10 They close their hearts to pity; with their mouths they speak arrogantly.