What is the way to automatically bill my users based on their usage?
I need to bill the user behind the scenes a variable amount every month without any action from their side.
PayPal's subscription model does not work because the amount changes every month based on usage.
Is this possible with PayPal?
You will need either 'Reference Transactions' on the PayPal business account -- or the Braintree gateway. Contact PayPal at https://www.paypal.com/smarthelp/contact-us or https://www.braintreepayments.com/country-selection about approval for either.
If approved for you, either is its own specialized integration or v2 Vault API they should give you some guidance on.
(The PayPal v1 Vault API will not help you)