The correlation between obesity and income is not observably defined by a crisp linear relationship. A scatter chart that plots each state's obesity rate vs. its average income demonstrates that for those states whose average income is greater than $50k per year the correlation between a state's obesity rate and its average income is effectively zero.
For states whose average income is less than $50k per year, the picture is somewhat different. There is an observable negative correlation between obesity rate and average income. This is particularly evident for states in the Deep South, followed by states in the lower Midwest and perhaps less noticeably southeastern states.
Surprisingly, the obesity rate of 22% reported for Hawaii gives this state the third lowest in the nation.