There are all sorts of work at home jobs out there, from business opportunities to steady employment with companies, to starting your own company. If you're like many people, succeeding at your own business or investing in a business opportunity isn't what you need. When you want to find work at home jobs that pay weekly, you will need to search for those types of jobs, which is completely different than looking for business opportunities or start-up companies.
You can find listings for traditional work at home jobs that pay weekly all over the internet, on sites like Monster, CareerBuilder, CraigsList, and even specialty sites designed for particular niches and interests in working at home. These jobs will usually be listed as hourly or salary positions, and will offer a more stable position than a business opportunity or project-based job. When working at home for these types of companies, you'll usually be required to file a W-9 form, so that you can pay taxes at the end of the year. Some of these companies will pay you by the hour, which is hard to track when it comes to working from home, but can be done. Other companies will have a salaried rate for you on a weekly or monthly basis, dependent upon what you get done or how much you work. Again, this isn't easy to track, but many companies do offer this option.
The most common types of work at home jobs that pay weekly are ones that pay you on a project basis, but pay every week for what you've completed to that point. For example, I have this other writing project, and I do anywhere between 10-25 articles a day (it's not as much as it sounds like). At the end of the week, I get paid for all the articles I did that week. That way, I don't have to wait until the end of the month like a lot of companies want to do with their payroll.
If the payscale plays a large role in the job you want to find, you'll need to take that into account when you're searching for a work at home job. I have a position that pays bi-weekly as well, and from time to time I pick up other projects that are one-time gigs or on monthly payment schedules. So, you can find work at home jobs that pay weekly, you just have to be willing to invest the time to search for them. And if the job listings you find don't list the payment schedules in the listings, feel free to send in a resume anyway, and inquire about the option of weekly paychecks in your letter of interest.
Good luck, and happy job hunting!