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I'm not super knowledgeable on this subject, but I'll share what I run. I'm 280 pounds, and tour with some gear that isn't lightweight, on heavy steel framed bikes. This year we just got out for a couple of short bed and breakfast tours, but in the past I've gone on a few short cycle camping trips where my bike was quite heavy loaded with all my camping gear. Since I was solo touring I had everything for camping on my bike, I always fail at packing light and bring anything I think I might need and spares for everything, and I have yet to replace some of my camping gear with light-weight stuff suited for cycle-camping or hiking. Long story short, I put a LOT of weight on my tires!
I use 26" wheeled bikes, but both the tires I run also come in 700C sizes. On my tourer I run Vittoria Randonneur Pros (26 x 1.5") front and rear. For my commuter, that I used for the B&B tours this year, I run a Rando Pro on the rear and a Panaracer T-Serv Pro-Tex up front. The Panaracer is nominally a 1.5 inch tire as well, but I purchased the 1.75" size knowing that they run small. I run it at the upper listed pressure for the 1.5" T-Serv, at 75 PSI. The Rando Pros I also run at the upper limit of their listed pressure at 90 PSI. Being as heavy as I am, and even when I'm commuting I'm usually carrying a load (heavy schoolbooks or lunch and workclothes), I seem to get a lot of sidewall deflection if my tires aren't pumped up pretty high. The Vittoria's seem especially good in this regard, and that's why I've got one on the rear of my commuter. The Panaracer doesn't have as stiff a sidewall as the Randos, but the higher rubber content makes it a little cushy for a front tire. Both of these tires have excellent puncture resistance.
I've successfully ridden both tires over all sizes of gravel and on bare dirt, loaded.
I wouldn't go too much higher than the recommended pressure for tires. Not only are they going to be overly stiff, but the manufacturers usually put a lot of research into the recommended pressures for their tires.
Hope that helps!