By taking a look at the first few weird numbers: $$(70, 836, 4030, 5830, 7192, 7912, 9272, 10430)$$ It is certain that prime numbers occurs more often within this range of numbers.
But are weird numbers more rare than prime numbers in the long run? Sure, by the definition of infinity, there are infinite prime numbers and infinite weird numbers. But if you calculated prime numbers and weird numbers for a finite amount of time, would prime numbers be more common than weird numbers?
This may not be very easy to explain, but I'd appreciate an attempt to keep it as simple as possible.