Because people are statistically more likely to keep paying for a service when they have set up a payment before hand. You're more likely to be ok with putting in payment information when you are simply signing up for a free service, however if you are putting in payment information to actually pay for the service at a later time you're much more likely to just let the free service run out. The less amount of effort required between a free service running out and a paid service starting results on a much higher chance of a customer staying for the paid service.
You're still signing up for the service. They just don't charge you for the first 2 weeks and you can cancel anytime before and it won't charge you.
Because people are statistically more likely to keep paying for a service when they have set up a payment before hand. You're more likely to be ok with putting in payment information when you are simply signing up for a free service, however if you are putting in payment information to actually pay for the service at a later time you're much more likely to just let the free service run out. The less amount of effort required between a free service running out and a paid service starting results on a much higher chance of a customer staying for the paid service.