Again, what good would that do? Obesity increases mortality across the board, this is widely messaged, and this continues to be widely messaged. Would increasing the messaging around obesity affecting Covid mortality specifically cause any significant difference in hospitalization? I highly doubt it. The same people who don't like the government suggesting that they should get vaccinated would eat fried butter balls in protest, and everybody else would continue as before.

Vaccination policies (including mandates), on the other hand, are proven to work and have immediate effect. They are the most logical choice.