Hurricane tie rafter supports

Although the knotted pine planks we are installing only weigh about 1.25 pounds per sq ft, I worry about the 2x2 rafters supporting the weight. Especially in the middle of the house where each rafter is end nailed to the center beam and not resting on the top plate as each does on the other end.

So I bought these 2x3 ties to connect rafters to beams fr my peace of mind,