Bruno Stillo, 2 years old, gets a therapy session on Friday at B&V Thera-Pro Associates in Miami as his mother, Jacel Delgadillo, left, watches. Cristobal Herrera for The Wall Street Journal

MIAMI— Jacel Delgadillo said she has tried a host of treatments to help her 2-year-old son, Bruno, cope with severe seizures triggered by a rare form of epilepsy, from a special diet to more than a dozen medications. But nothing has worked.

Now she hopes a legislative proposal in Florida will provide a new option: a marijuana extract called cannabidiol, or CBD, that anecdotal evidence suggests is effective in treating the disorder.

The substance, which doesn't produce a high and can be taken orally in an oil form, has been embraced by parents whose children, like Bruno, suffer from Dravet syndrome, which occurs in about one of every 30,000 births. The condition begins in infancy and can cause hundreds of seizures a day, developmental delays and even death.

"I'm praying that it becomes available here," said Ms. Delgadillo, a 37-year-old single mother of two in Miami. "It's our last option."

Lawmakers here and in a handful of other states are weighing measures to effectively legalize marijuana derivatives that are high in CBD and low in tetrahydrocannabinol, or THC, the psychoactive compound in pot. Among them are Republicans who otherwise strongly oppose authorizing the use of marijuana for medicinal purposes.

"I'm a converted zealot," said Rep. Matt Gaetz, the Republican chairman of the criminal justice subcommittee in the Florida House. He said he originally was against legalizing CBD because he thought it could open the way to broader use of medical marijuana. But after hearing the accounts of desperate families, he said he changed his mind.

"I will use every tool in the toolbox to ensure the parents of these severely ill children are not criminals," Mr. Gaetz said. He and others are preparing a bill in advance of the legislative session, which begins in March.

Similar efforts are under way elsewhere. Prodded by families, lawmakers in Alabama and Nebraska filed bills this month that would effectively permit the use of CBD to treat disorders like Dravet syndrome. Similar measures are expected to be filed in Georgia and Utah, according to legislators in those states.

Twenty states and the District of Columbia have legalized marijuana for medicinal use, but the states considering CBD bills, which are generally more conservative, aren't among them.

Yet the measures face obstacles. In Florida, a separate initiative to get a medical-marijuana amendment on the ballot in November has met with stiff opposition from GOP leaders, including Gov. Rick Scott. The petition drive has secured the necessary number of voter signatures, but the ballot language must still win approval from the state Supreme Court.

State Rep. Dennis Baxley, the Republican chairman of the House judiciary committee, declined to support a request by Mr. Gaetz to include a CBD bill in a package of criminal-justice measures, a move that would have boosted its chances.

"It's noble that he wants to figure out how to help these families," Mr. Baxley said. But "we need to figure out if this is really safe."

There is no scientific data on the effectiveness and safety of CBD to treat seizures, said Elson So, president of the American Epilepsy Society. Though anecdotal reports about the oil are encouraging, he said, "it would be premature" to authorize it as a treatment. A preliminary study on CBD, led by a New York University researcher, has just begun, Dr. So said.

Meanwhile, parents of some children with the ailment have moved to Colorado, where marijuana is legal and they can obtain an oil derived from a high-CBD and low-THC strain of pot dubbed "Charlotte's Web." The variety is named after Charlotte Figi, a girl with Dravet syndrome who stopped having seizures and became more functional after taking the oil.

Roughly 300 kids and adults with a variety of disorders are using Charlotte's Web, said Joel Stanley, whose family grows the strain, along with others, and owns marijuana dispensaries in the state. Demand is so high that there's an in-state waiting list of 300 people and an out-of-state list of more than 1,000.

Virtually all the kids suffering from seizures have responded in some way to the treatment, which costs an average of $70 a week, Mr. Stanley said. Among them are Cristi Bundukamara's 14-year-old son and 13-year-old daughter, both of whom have a rare neurodegenerative disorder. After two months of CBD treatment, she said, her son's seizures have decreased by half and her daughter isn't having any.

Stories like that give Ms. Delgadillo hope. She had been planning to move to Colorado, but is now waiting to see if the Florida legislature acts. Her son Bruno has been on medication since he was 3 months old and cannot speak or sit up. Because he can have a seizure at any moment, she never leaves him alone and sleeps beside him, holding his hand.

With CBD, "maybe my son will be able to sit up or take a few steps," Ms. Delgadillo said. "If I could just hear 'Momma,' it'll be a miracle."

Write to Arian Campo-Flores at