The Bersa platform is nothing more than a PPK with some mods. This means that the safety needs to be left on when carrying chambered, otherwise if it falls someone might get shot. It also means a solid metal gun, not the lightest thing out there, about 25 ounces loaded if I remember right. And even with that added heft, the recoil might seem pretty stout since it's a blowback gun, don't know how important that might be for you.
When open carrying you also need to be using a retention holster. Even if we disregard the fact there aren't a great many retention holsters for PPK type guns, there is still the fact that you'd have 2 potentially troubling steps to get your gun going, very troubling actually since I believe that Bersa doesn't make guns with left handed safeties, though I may be wrong. And obviously with open carry, a potential need to draw would be in the very biggest of hurries.
When you lastly factor in that the round the Bersa fires has half the power yet twice the cost of 9mm, it becomes difficult indeed to suggest any reason why you should get it as an OC gun. If you're alternatively okay with DAO, want cheap and light yet reliable, and .380 or better, you should probably take a look at Kel Tec's guns.
The Glock will have more power yet less recoil, certainly more holster options, no safety to fumble over and a consistent, more easy to master trigger system. But the big problem I see there for you is that they still weight well over 20 ounces loaded.
I just googled the weight of the subcompact 9mm XD's and it appears they are 20 something ounces unloaded, indicating pretty much all of these are heavier than it sounds like you're looking for. So I will again say that this is a further reason to consider Kel Tec's as the light weight option, if weight and reliability are the primary concerns you have.