Tires and body position will have the biggest effect on flats. At high speed, it will be mostly body position (aerodynamics). At lower speed, it will be more the tires. Skinny high pressure tires will be faster on smooth pavement. Fatter, lower pressure will be faster on crappy or unpaved roads. IMO, 23mm and lower tires are ideal on a 700c rim if you have a chase car carrying a spare wheel. Most club riders use a 23, but if I'm doing long rides on unsanitized roads without a team car, I'll be faster on average with a bigger tire that doesn't flat as much.
As for weight, your effort will be proportional to total mass on a slow steep hill. So, if you, your bike, and your gear weights 200 lbs, then for each lb you take off the bike, you will climb the hill 0.5% faster. If you are touring and your total ride weight is 250 lbs, then you will climb 0.4% slower per lb of extra crap (that is 0.06mph at 16mph).
On a very hilly ride, your overall speed and ride time might suffer by those percentages. On a typical ride, it will be somewhere between 0 and 0.4% per lb. There are plenty of speed calculators on the net if you want to play around.
Flip the stem on the fuji, and put your road bike wheels on it (assuming compatible). Then do a few time trials on your favorite loop.