Will I lose mileage...

I have seen it reported that due the slightly wider tires on the 16"
Touring rims, a computed 1-2 MPG reduction is to be expected.

FWIW, my experience is that there are 1001 other variables in play
and it is difficult, if not impossible, to isolate the touring tires as the
cause of such a small MPG reduction in daily driving.

 

The 15/16" measurement has to do with the size of the wheel rim,
and with some adjustments the diameter of the tire at the bead, its
inner edge.

Both the standard OEM 15 and 16" tires have near identical tread
circumfrences, so no correction of the MFD/speedometer is necessary.

 

In a nutshell, yes. You will lose some fuel efficiency due to weight and likely due to tire choice.

Even swapping to new tires with your stock wheels will usually incur a MPG loss for the first couple thousand miles or permanently until you choose a different tire.

It is just the price you pay for better handling or appearance.

The only real way to avoid this negative penatly is to:

A. Learn how to drive more efficiently to make up for any losses
B. Purchase a set of 16" wheels that are lighter than your stock wheels and choose a good low rolling resistance tire that is also lightweight and not too wide.