My weight depends on the time of the year, but me+all the gear is almost always 300 + lbs.
I run deep V Velocity Dyad 36h rims with solid spokes and deore LX hubs. Tires are bomb proof Vittoria Rubino 700 x 28 at around 110 psi rear, and 105 front. They are at or little over their max psi rating...for the last couple years.
Fast rolling, quiet, not too heavy, puncture proof so far after ridding on everything for few k miles. They are also great on wet.
I have to add that I have Specialized Crosstrail hybrid with front suspension, and Cane Creek Thudbuster suspension seat post for comfort. I think that helps a lot while running skinny tires for my weight.

PSI is more accurate, but I see you are using BAR...You are in US, so I wonder why its your choice?

If anyone is interested in converting PSI/BAR http://www.centauro-owners.com/articles/psibar.html

Its not you...its a fact. I noticed that the reason of my "bad day" was always a low/er/ pressure. Its a huge difference in feel between 110PSI and 95-100PSI. It's always a good idea to check the pressure before each ride. Checking by hand is ALWAYS off lol

Numbers on the Bar scale are bigger on my p/v gage that goes along with the (frame fit)pump.

had TR tubes .. they let you know when the pressure drops , the rolling resistance is noted.

[But the whole 10 month trip was puncture free.)

Schwalbe One in 700x25. Fast. Comfortable. Good/great cornering grip. Light. They measure closer to 27mm on my rims. I am sold on these tires especially running latex tubes.

Have a set of Challenge Paris-Roubaix 700x27 that are really more like 31mm wide. I haven't had them out yet but they should be fast and comfy given the casing is the old Clement Criteriums (not the Setas). They are heavy.....305gm actual. If they are as fast as the Schwalbe and more comfortable, these will prolly be my go to sneakers.

A Clyde running 20-23mm width tires in the rear needs a lot of pressure.......120-150psi (8.5-11.75 Bar). Running 28mm tires drops the required pressure down considerably.....maybe 90-100 psi to get the correct patch or the so-called tire drop.

Some high quality tires at 32mm width tire on the rear will be much more comfortable and roll better than any 20-23mm tire for a heavy rider

Until about 3 weeks ago, I was around 265 (now 254 and dropping fast) and have been running Vittoria Open Corsas 23s on Easton EA70 wheels at around 135-140psi depending on the conditions. The first set I had on lasted a long time and seemed relatively puncture free. With a newer set on now, I seem to be getting alot more flats, although it could be because I have been riding more in the rain lately. I used to ride Vredestein Fortezzas before the Vittorias and they were nice and fast as well. Vredestein used to make a tire called something like Fortezza superlight or ultralite. It was the fastest tire I have ever had on my bike, and I nearly cried when I had to give up and take them off when they wore out. What I like about the Vredestein and Vittorias is that the rated max on the tires is 145 psi. So you are not going beyond the design pressure for the tire to run tham at 135-140 psi. If I use the Vittoria tire pressure chart for my weight, it recommends 140 rear and 135 front. I got a set of the Vittorias for my wife, who had been running on Hutchinson Fusions, and she was amazed at how much difference simply changing tires and increasing her pressure by about 10psi made in her speed. The downside is that they are more expensive and are not the most durable tire, so you will have to replace them more often. But that is a price I am willing to pay for now. I like to go fast and if I pay an extra $15 per tire once per season to get it, I consider it money well spent.

140 psi...yeow! Doesn't that feel like riding on steel?

Tire charts for different sized people.

Not really. The Vittorias have a much higher thread count than most tires (320 vs 50-100 for most tires) and as a result are much more supple, even at higher pressures. Yes, on particularly rough roads, it can get a bit rattley, but on smooth roads, which is most of what I ride on, it is not noticeable, except for being much faster coasting and rolling downhill.