I think the primary problem you are seeing here is that you are trying to pick up ordinary paper, which is relatively porous. When I was working with suction cup systems we were dealing primarily with labels, so non porous, waxed backing paper. Our page turning systems used rubberised rollers rather than suction cups, even though we used pneumatics elsewhere in the page turning mechanism.
As the two videos show, with the waxed paper only one sheet at once is usually picked up, whereas with the more porous tissue, several are usually picked up. In fact the vacuum is so strong that with only a single tissue, the demonstrator was having trouble separating the suction cup from the table below.
I agree with morbo that your system has way more suction than it needs, but I think it's probably easier to find the right balance experimentally than to try to work out from first principals, with all of the variables that aren't accounted for by the math. I think you need to get a stack of paper and your actuator (and possibly some alternatives) and find the limits of your system.
You need to be able to control the vacuum
Without being able to control the vacuum you are going to have a hard time controlling the behaviour of the system.
As in the videos, you need to be able to see what the vacuum pressure is when picking up and holding the paper, so you need a relatively accurate vacuum gauge.
Depending on your characterisation of the system, you may only need variable vacuum control while performing that characterisation, but it may be that you need to vary the vacuum dynamically during different phases of your pick & place operation. Rather than just on/off you may need low vacuum to pick and lift a single sheet, followed by a switch to high vacuum befor a fast move to the place location without dropping the paper.
How a variable vacuum is achieved is beyond the scope of this answer, but may involve a variable vacuum source, a variable regulator, a bypass or some king of pulsed source or bypass. The specifics are beyond my expertise. What I do know is that you need to characterise the behaviour of your system.
Characterise the behaviour of your suction cups
Starting from a pressure too low to pick up any paper steadily increase the vacuum until it picks up one sheet. Then keep increasing the vacuum until it picks up two sheets. The vacuum at the mid point between the two should give you a good quick compromise between holding a single sheet securely and the risk of picking up a second sheet. Depending on the reliability you need though (99%, 99.9%, 5 nines) you may need to characterise your system more thoroughly.
Repeat a pick-up attempt at each pressure enough times to build up confidence in how much variation there is in results. If vacuum $x$ picks up 1 sheet 99% of the time and never picks up 2 sheets, while vacuum $y$ picks up 1 sheet every time, and 2 sheets 1% of the time you can surmise that you have a well characterised system and can probably rely on the midpoint to pretty reliably only pick up 1 sheet.
If vacuum $x$ picks up 1 sheet 80% of the time and 2 sheets 20% of the time, while vacuum $y$ picks up 1 sheet 20% of the time, and 2 sheets 80% of the time, then you may have to consider whether this is the right solution for you.
Check it behaves the same at the extremes
It may also be worth checking if behaviour is different when the stack of paper is full compared to when it is empty. If not, then you may have to chose a different compromise point to maximise the reliability over the whole paper refill lifetime. Alternatively, you may have to calculate vacuum pressures at the pick location depending on the number of sheets in the stack (if you can't mechanically compensate for the stack height, as printers do).
Finally, you may want to try running the same characterisation with 70gsm and 90gsm paper as well as at 80gsm. While there is little variation in commercially bought paper, you can never rule out customers choosing to buy cheaper thinner paper, or decide they need to use heavier paper stock for some jobs.
In my experience it's better to know about likely problems before they occur than have to deal with them in the middle of the night.
Frantic Customer: We filled the machine & it started picking up 2 sheets at once!
Bleery eyed Engineer: What did you change?
Apologetic customer: Oh, this job needed 70gsm paper
Resigned engineer: Ok, go into the .ini file and reduce the vacuum value by 20% then on Monday put in a change request to implement 70gsm paper support in the GUI
Conclusion
Reliability only comes from testing, and testing again after every adjustment you make. Data gives you the ability to reason about the behaviour of your system, predict what changes will improve or impact on reliability and test hypotheses until you get what behaviour you need, or decide you need to a different solution.
