As a question, why does what he is using the bandwidth for matter? As a tenant, I'd be livid if my landlord decided whether my usage of the internet was valuable or not. Does anyone else's landlord decide if their choice of internet content is worthy of then bandwidth required to view it?
If you are worried about pirating, take steps to limit that, don't use that as a red herring since he apparently has enough bandwidth to do that with the current usage.
If your concern is your accountant wanting to know why you want a bigger cap, the appropriate answer is that one of your tenants is asking for more bandwidth, nothing to do with what the tenant is using it for. I'm not sure how this is different from any other use of the internet by your tenants, whether to have a video conference with their dying relative or otherwise.
Are you being inflexible, yes, you appear to have decided you don't think it's worth doing because of the content he views and thus won't do it. On the other hand, being inflexible is certainly your right. If he will pay the difference and then pay any fees to upgrade or downgrade, it doesn't seem to me to be a big issue, but again, you have the right to refuse.
You can certainly just say that he can work within the terms he agreed to or leave since the internet issue isn't changing.