Your tyre size increased by a %age will also increase the distance travelled according to that percentage, whereas the odo will show the mileage according to a shorter tyre size as it is programmed to factory size i.e: 175/65/R15
Given that the size of a 195/65/R15 would be 3-4% larger, therefore each rotation of the wheel covers more distance by that much.
Mileage drop should be negligible in reality.