A larger contact patch will create more rolling resistance. Increasing tire pressure reduces contact patch size, decreasing pressure increases contact patch size. Tires with softer rubber have larger contact patches than tires with harder rubber. Wider tires have a wider contact patch, and therefore more rolling resistance. But there are people here who think that bigger tires have less resistance because they can absorb road irregularities, small debris, and gravel, this is opposite to reality. But then for centuries people insisted the world was flat, and sometimes killed or died to support their belief in this "fact."
At one time I was a distributor for Pirelli tires, the company had been conducting studies on new features to increase fuel efficiency through tire design, and marketing these tires to auto manufacturers in order to help them meet mandatory fuel mileage standards. Wider and softer tires must always come at the cost of increased rolling resistance.