Webalyzing works very fast to crawl your site as quickly as possible. However there are many factors that can influence exactly how long it will take.
When you log into your dashboard as a new subscription you may see the following warning when viewing your sites analysis:
Within a few moments of submitting your website our crawlers immediately go to work to begin analyzing your content. As we discover new pages, they will be added to queue to be analyzed as well. As soon as a page is finished being analyzed it will be made available for you to display.
Small sites that only have 30 or less pages could finish there analysis in under an hour. Larger sites with thousands of pages could take several days to crawl each one. In either case the timing depends on how much content is found on each page and how busy the crawlers are at the time of submission.
Paid subscriptions do get priority in the queue over free subscriptions. If you would like results faster, you may want to consider upgrading your account for faster processing.