Weirdness budget is the idea that when you are learning something new, there are only so many unfamiliar concepts that you can handle without getting frustrated or confused. It's easier for us to learn one thing at a time instead of getting bombarded by lots of new ideas that don't align with our current practices or ways of thinking.
This means that when you are building a new product, you should avoid making things any weirder than they need to be. You have a budget for weirdness and you should spend it wisely.
Of course, weirdness is subjective. What's weird for us can be normal for others. Part of understanding your customer is knowing what's weird for them.