SAN ANTONIO — The broadband era began with the expectation that Internet connections were like buffets — all you can eat, 24 hours a day. But users are now being prodded to think about how much they’re consuming.

Here in South Texas, Time Warner Cable customers have been given the online equivalent of a scale in the bathroom, a “usage tracker” that adds up all the household’s Facebooking and YouTubing. Customers who sign up for a light plan of 5 gigabytes of broadband — that’s the equivalent of two high-definition movie downloads — are rewarded with a $5 discount each month if they don’t go over. If they do, they pay $1 for every additional gigabyte.

“We’re moving away from one-size-fits-all,” said Jon Gary Herrera, a Texas spokesman for the cable company, which now tends to call itself a broadband company instead.

Some of Time Warner Cable’s competitors are moving the same way, slowly but surely, toward tiers of pricing for higher speeds and bigger amounts of broadband at home, mimicking the wireless industry’s much-maligned pricing plans. The strategy, called usage-based billing, is advantageous for the companies that control the digital pipelines. But it may be detrimental for customers who are watching more and more video on the Web every month, as well as companies like Netflix that distribute it. Some fear that as customers become more aware of how much broadband they’re using each month, they’ll start to use less of it, and in that way, protect traditional forms of entertainment distribution and discourage new Internet services.