Ok Tires then.
Narrow tires have a small contact area, which increases the pressure over the contact area, and has less rolling resistance.
Wider tires have a large contact area, less pressure over the contact area, and have more rolling resistance. They also have a larger rotational mass.
Narrow tires are good for pavement where a smaller contact area is beneficial in retaining traction in bad weather, and increased gas mileage
Wide tires excel off-road because of the wider contact area, and less pressure over the contact area. Notice AG equipment does not have pizza cutter tires. The wider tire allows that equipment to avoid digging into the soil and possibly getting stuck.
Going from 10.5" to 12.5" is a judgment call. The wider tire may require changes to backspacing and fender flairs to stay legal on the road.