According to this verse, fat is trouble. Near the end of Moses' life God warned the people of Israel that their future prosperity would be the cause of their spiritual downfall. God had promised that if they would obey his commands, they would be prospered in every way. Yet while prosperity is a blessing from God, it undermines the spirituality that led to it.
Prosperity in this verse is pictured specifically in terms of food. After years of living in bleak wilderness conditions where they had to completely depend on God for food and water every day, they would live in their own land, build homes, and grow their own food. Under God's blessing, their agricultural efforts would be successful, resulting in a bountiful harvest. Lots of food means lots of eating. Lots of eating means getting fat.
The problem with fat in the way God speaks of it here is that it creates the illusion of sufficiency. Being fat is a condition whereby our bodies carry a great deal more substance than we require to survive. The lack of need of food translates consciously or unconsciously into a lack of need of God.
Notice that God is speaking primarily to the nation, not individuals. He is not saying that people who eat too much automatically turn to other gods. He is speaking about a nation that becomes full and grows fat. He is speaking about what would happen when his people as a nation are prosperous. When a culture has much more than it needs, its relationship to God is in danger.
There are many societies today that could be categorized as fat. Not only are the waistlines of these societies larger than the world average, their overall lifestyles could be called fat. These are those societies that are able to give themselves to an abundance of things and activities that are not essential to living. That these societies may perceive their luxuries as necessities, is a further indication of how fat they really are.
Only societies that are fat struggle to lose weight. Fighting fat is an impossible battle, not because we cannot learn to effectively diet, but because fat is more than about individual choices and more than just a diet issue. Fat is the result of a selfish society.
When God called Abraham, he promised to bless him and make him a blessing (Bereshit/Genesis 12:1-3). The purpose of receiving God's blessing is to bless others. The purpose of prosperity is not personal success and comfort, but it is to be the means by which we alleviate the needs of others. To successfully fight fat we don't need a diet plan, we need a plan to die to self. We need a completely different way of looking at life: one that puts God and his ways first.
Prosperity is not the problem. We are. Our natural spiritual condition cannot handle God's blessings. Instead of administrating his blessings effectively, we get fat on them instead. The Torah understands this, thus preparing our hearts for the needed transformation that only the Messiah can provide. His life confronts our fat lifestyles. His death provides forgiveness. His resurrection frees us to live fat-free lives.