Fatter tires tend to have lower rolling resistance and lower pressure.
I have some 60mm slicks that have similar rolling resistance (~10 watts) as my 23mm road race tires.
I've gone as low as ~40mm, but below that you are just dropping the bottom bracket real low and getting a stiff ride. Its not faster. I've used 25mm tires on my mountain bike, but it was just ugly and inefficient.
I would recommend some 45mm gravel tires (Panaracer or Schwalbe make some good ones).