Microsoft deliberately won't tell you what the size limit of your Live mailbox is. They sort of imply it's unlimited. This is a smoke and mirrors game in which they can shift the goalposts any time they like and is similar to how they very quietly announced they were chopping OneDrive storage from 15 GB to 5 GB. They have in fact twice chopped OneDrive from a large amount (it was 25 GB at one time) to a smaller amount, and obviously twice gone from a small amount to a large amount.
The reason we were given for OneDrive being chopped was that they had had a period of unlimited storage and a small number of people abused it, so now they had to chop everyone to 5 GB. There was no explanation why they couldn't go back to 15 GB. Well, I just opened a new Gmail account and moved everything to Drive.
Going back to Live Mail, as soon as you hit some sort of limit, you'll keep getting these emails saying your Outlook account is growing too fast. Even if it's growing really slowly. I don't actually know what the limit is except that I keep getting these messages, and there is no actual way to know how much space my emails have used. I am actually getting to the point of being annoyed by the messages, and have now started moving mail off the Outlook.com server to another Gmail account. Maybe I will start redirecting new mails to that account as well.
It looks like this capacity limit for Live could be as low as 2 GB - compared to the 15 GB mailbox that Google gives you it is not much, and there isn't a lot going for MS's cloud services now that OneDrive only stores 5 GB.
