Three years ago, Newton joined a growing number of Massachusetts communities banning supermarkets and other large retailers from providing customers with thin-film, single-use plastic bags at checkout.

Some stores in the city now offer a new kind of plastic bag — one that’s heavier, made of recycled material, and designed to be used at least 125 times.

Will this “reusable’’ bag reduce the stream of discarded plastic that ends up on sidewalks, in landfills, and choking the ocean?

Some in Newton are skeptical.

“Really the key is for people to bring their own bags,’’ said Alison M. Leary, city councilor at large, who headed efforts to pass the bag bylaw.

At least 81 cities and towns in Massachusetts have implemented rules that ban or impose limits on the use of disposable, single-use plastic bags, said Brad Verter, founder of Mass Green Network, a volunteer environmental advocacy group.

“Things have been going just gangbusters . . . the will is already out there,’’ Verter said. “Everyone already knows that plastic is bad.’’

But as these local laws become widespread, advocates are pressing the Legislature to adopt statewide regulations with consistent instructions for retailers, and tighter limits on what qualifies as a “reusable’’ tote.

On July 12, the state Senate approved a ban on plastic checkout bags as an amendment to an environmental bond bill. Starting in August 2019, a reusable grocery bag would be defined as a sewn bag with stitched handles that is designed for at least 175 uses, can carry 25 pounds over a distance of 300 feet, and is made of cloth or other machine washable fabric.

“It’s critical. You’re seeing more and more the impact of plastic waste on the environment,’’ said Senator James Eldridge of Acton, who filed the amendment with Senator Cynthia Creem of Newton. “It’s a common sense measure that Massachusetts should be leading on.’’

For the amendment to become law, the House also would have to agree to include the rules in a final version of the bond bill, which would then go before both the House and Senate for a vote prior to the conclusion of the legislative session at the end of the month.

Meanwhile, retailers and municipal officials are wrestling with how to interpret local restrictions.

At the Star Market in Newtonville, heavy reusable bags made of recycled plastic are available for free at checkout, alongside paper bags.

Printed on the bottom are instructions: “To clean, rinse bag and hang upside down to dry.’’ And in giant letters on the front is the rhyme: “Use me re-use me & try not to lose me.’’

The plastic used in the bags is thick enough to fall outside Newton’s disposable plastic bag ban, acknowledged Leary, the city councilor, but she said the city’s goal was to curb the practice of giving customers plastic bags at checkout.

“They’re legally in the law, but not in the spirit of the law,’’ Leary said.

Shaw’s, which also operates Star Market locations, participates in efforts to promote recycling and other programs in its Greater Boston stores, offices, and distribution centers, according to a company statement to the Globe.

“We also have available at our stores other shopping bag alternatives that further promotes the use of reusable bags,’’ the statement said.

The chain has paper bags available at the Newtonville Star Market store, said Teresa Edington, a company spokeswoman.

Brian Houghton, senior vice president of the Massachusetts Food Association, which represents grocery stores and supermarkets, said the group’s members would favor consistent statewide rules.

He said members would support regulations that impose a fee to use paper or plastic bags, and encourage customers to switch to reusable bags.

If the state Legislature does not take action during the current session, Leary said she will propose amendments to Newton’s bag bylaw on Aug. 1 that will toughen standards. The amendments would expand the regulations to apply to all retailers, regardless of size. The city’s existing rules are limited to retailers that operate at least 3,500 square feet.

The amendments also would impose stricter standards on the design of reusable bags, and impose a 10-cent fee on the use of paper bags, Leary said.

“It’s clear that if you don’t make it a requirement, they won’t do it voluntarily,’’ Leary said.

Lise Olney, a member of Wellesley’s Natural Resources Commission, said officials in her town imposed stricter standards based on Newton’s experience with its plastic bag rules. The Wellesley ban, which went into effect in 2017, limits “reusable checkout bags’’ to sewn bags with stitched handles that are machine washable.

“We were able to learn from their experience that big retailers were trying to skirt the regulations by using those [thicker plastic] bags,’’ she said.

John Hilliard can be reached at john.hilliard@globe.com.