[BinahYeteirah]

Yes, the Moby becoming loose is a common issue. As she gets heavier, this is likely to become more pronounced. Usually stretchy wraps are best for smaller babies. If you like the wrap, you could get a woven wrap. They don't stretch out and the knots don't generally slip if they're tied tightly. I can't recommend a specific brand; the one I have is a WAHM tester. I do know some of the nicer woven wraps can be super expensive, so if you're on a budget, you could even use a simple length of cloth. Google would probably be useful for measurement recommendations and other instructions.

I know nothing about the Becco, so I definitely can't help you there.