"So, you are come at last! I began to think I should never see you. I am so ill I can hardly speak. I have not seen a creature the whole morning!"

Visitors naturally do cheer you up, as Mary shows - but if you don't reciprocate with a more cheerful manner, they wont come again, as Louisa et al show. IMVHO Mary's "illness" has something to do with pregnancy, I've always taken this passage as a good empirical description of morning sickness. One minute you feel like a rotten potato and not up to seeing anyone, and the next you're feeling fine and want to share your misery with everyone else. Its something that the single Anne has been implicitly excluded from, and actually makes her feel left out; its like she's saying "I'm so stressed... but then YOU don't have anything to be stressed about, you has-been".

There's more to it than that though. She's using it as a weapon to monopolise Anne's attention and use her as a blank canvas to do with as she pleases, such as moan in this instance; it also actually has the opposite effect of making her seem less important, because it demonstrates how useless she is at organising herself and her family into comfort, whilst Anne is a natural. Its also a portrait of the miserable fate that would have awaited Anne had she married Charles - eventually, the novelty would have worn off and she'd have been forgotten about, with only illness or childbirth to make her stand out. You could argue it would have been her duty to get on with life, not expecting the honeymoon period to last, but imo the possibility that she might very well be feeling sick makes it more poignant and ironic.