“He offered the tribute.” More literally, “He brought near the tribute.” The text is using sacrificial language.

“a very fat man.” Eglon is the only man who is named and specifically called “fat” in the Bible (although the High Priest Eli is called “heavy,” 1 Sam. 4:18). And Ehud is the only man in the Bible who is named and called “left-handed.” So this is a conflict between two unique men: lefty versus fatty. Looked at another way, being left-handed was a terrible cultural disadvantage and considered a curse, while the fact that Eglon was fat showed that he had the best of life: a sedentary lifestyle and loads of food. So this record subtly shows that being disadvantaged but with God is always better than being worldly advantaged but without God.

It is worth noting that although the Hebrew word translated as “fat” here in Judges 3:17 is occasionally applied to humans (Ps. 73:4; Dan. 1:15) it is used primarily used of animals (e.g., Gen. 41:2-4, 18, 20; 1 Kings 5:3; Ezek. 34:3, 26; Zech. 11:16). That Eglon was “very fat” reminds us of the “fatted calf,” a calf that had been purposely fattened up for slaughter (Luke 15:23, 27, 30). Thus that Eglon is specifically called “very fat” adds to the motif of sacrifice to God that permeates the Ehud-Eglon record (see commentary on Judg. 3:12). Daniel Block writes: “Eglon is portrayed as a fattened calf going to the slaughter.”^a

It is also worth noting that the word “fat” is used of the minds of people who are stubborn, stupid, or unresponsive to truth (e.g. Isa. 6:10), and although the word “fat” is not specifically used of the minds of Eglon and his men, that was certainly the case. For example, Eglon was mentally “fat” (stupid) when he dismissed his bodyguard with Ehud in the room, and, frankly, the bodyguard was stupid to leave or go far away.