So your solution to the obesity problem is to make food more expensive? Yeah, that's kind of dumb.
A lot of the people who are obese are that way because they eat lots of food that isn't exactly healthy. Quite often that kind of food is what is actually really cheap to eat. If you raise the cost of food, then the price of the healthy options also increases. That puts those options further from the reach of those who have less money, and so they'll be even more inclined than before to eat the cheap, unhealthy options because that's what they'll be able to afford.
I disagree with this premise. If you cook at home eating healthy is pretty cheap. An entire head of lettuce costs $1-$2 depending on where you live. A good sized vine ripened tomato is what $2 maybe. You could serve your family one salad a day for a month without breaking the bank. Water is free. Eggs are pretty cheap. White egg yolk is a good source of protein. Whole grain bread isn't exorbitantly expensive. Oatmeal is cheaper than lucky charms. Fat free milk isn't expensive.
Food in this country is definitely too cheap. The OP has a good point. The only problem is certain niche products like strawberries would definitely shoot up way up in price. Strawberries are not a staple so I could definitely see their use falling. But even if the price of lettuce doubled I don't see myself really even noticing.