In my own system I would open the actual hand with 2♥, but not showing weak 2 but both majors and BELOW opening strength. I would pass the second hand as we have no bid to show weak 2. Your theoretical hand I would gladly open a weak 2 if available in the system. That doesn't necessarily mean that you have to open 1 of a suit if you add a little strength. I like to have full values for my opening bids. Hate to see partner's disappointment when laying down a dummy which doesn't agree with his expevtations. If we end up in a NT-contract partner might not be happy, expecting more