(easy) use platinum pieces (worth 10gp) to decrease the weight.
(slightly more work) buy gems or semiprecious stones. Every GM I've encountered would allow you to use these in lieu of coinage, but I suppose it's possible you'll run into one who would claim you had to sell the gems for half what you paid for them ...
(expensive) buy a handy haversack - that would let you carry up to 60,000gp value for a total weight of 5lb. Oh, and you could use it to hold other things as well if you don't have that much coinage!
Just tell HeroLab to ignore the weight, and tell any GM who gets upset that you're allowed to leave stuff "at home" while you're on a mission. I haven't bothered with coins yet, but that's where my cold weather gear, climbers kit, &c. stays unless I'm on a trip that requires it. (For HeroLab, I just set those items to "dropped to the ground").
You can use the Custom Location in the Gear tab to make your Absolom home/storage locker.
That is also where I use the Custom Valuable to make things like the 50 gp Courtier's Jewelry needed to make the Courtier's Outfit work correctly.
I just wish the printouts would organize items by container. Would make so much easier for my 12th level archer with 3 containers with arrows in them of multiple types.
And a Handy Haversack won't be available for a new PFS PC. Not enough Fame, yet. However, if you have access to the Adventurer's Armory, there is an item called a Masterwork Backpack that is mundane, so always available, which gives a small boost to Strength, but only for carrying capacity. And Hero Labs actually calculates it in, when it is checked.
In general, in my experience, few GMs worry about coinage weight in PFS. I have it turned off on all my PCs, so I don't have to mess around with converting gp to pp, or other low weight items of value. Then again, most of my PCs seldom have enough weight in coinage to worry about. Easy come, easy spend...
Why not? I'm okay with the assumption that you can store wealth "back home", but if you want to have it available, on your person, to spend it has a weight just like any other piece of equipment.
I keep track of all of my equipment, even when it means my characters suffer because of it.
Although I do wish we'd get a solid ruling on gems/art objects. Is a "1000gp gem" sold for 1000gp or 500gp? I was hoping Ultimate Equipment would list them under "trade goods" but alas, it did not.