The Maryland House of Delegates. (Patrick Semansky/AP)

The Maryland House of Delegates advanced more than 125 bills on Saturday, including measures to legalize medical marijuana and to make “cyber bullying” a crime, as the 90-day legislative session headed into a very busy home stretch.

Meeting in a rare Saturday session in Annapolis, the House also passed a measure to crack down on toll violators but balked at a proposal to allow all Maryland counties to impose bag taxes.

With two weeks remaining, a crush of bills remains on the General Assembly’s agenda. Among them: high-profile gun-control legislation, a measure that would allow illegal immigrants to obtain driver’s licenses and an attempt by Prince George’s County Executive Rushern L. Baker III (D) to take over the county’s public schools.

“I think we all anticipated a fairly low-key session, but several hot-button issues have emerged that we’re dealing with, and there’s more to come,” Del. John L. Bohanan Jr. (D-St. Mary’s) said about this year’s session, during which lawmakers also repealed the death penalty and are close to passing the state’s first gas tax increase since 1992.

The activity Saturday came in advance of a Monday “crossover” deadline for bills to pass in at least one legislative chamber; otherwise, they face a procedural hurdle that often means defeat. The Senate, which did not meet Saturday, is scheduled to return Monday.

During the House’s long Saturday meeting, takeout food piled up in the chamber’s lounge, and Speaker Michael E. Busch (D-Anne Arundel) wore tennis shoes with his business suit to make the hours of standing at the lectern less uncomfortable.

The medical marijuana bill, sponsored by Del. Dan K. Morhaim (D-Baltimore County), would allow a small number of academic medical centers to distribute marijuana to patients beginning in 2016. The centers would be required to monitor patients and publish their findings, an approach that officials in Gov. Martin O’Malley’s administration have characterized as cautious enough to win their support.

The legislation is expected to get a final vote in the House on Monday before moving to the Senate. “Hopefully it will pass and will help sick people in Maryland who need compassionate care,” Morhaim said.

Some lawmakers, including Del. Adelaide C. Eckardt (R-Dorchester), said they remain uncomfortable with the idea, however. “I don’t want us to end up like California,” Eckardt said. “We’re trying to teach people alternatives from a . . . substance-using society, and this goes against that whole argument.”

Legislation passed last week by the Senate would decriminalize possession of small amounts of marijuana, making violators subject to only a $100 civil fine.

The House also unanimously approved a measure Saturday designed to make cyber-bullying a crime. The bill was introduced after the suicide last year of a 15-year-old Howard County girl. The girl’s family said she took her life after being harassed online.

The case sparked international interest. American Idol stars sent out tweets of support, and Baltimore Ravens running back Ray Rice campaigned on behalf of the measure.

Under the legislation, creating a fake profile, posing as a minor, posting real or doctored images of a minor and signing up a minor for a pornographic Web site would be misdemeanors punishable by up to a year in jail and a $500 fine. A similar measure is pending in the Senate.

The House also voted unanimously to pursue more aggressively toll violators on the Intercounty Connector and other roads where motorists pay via E-ZPass transponder.

The legislative push came after The Washington Post reported in September that nearly 650,000 vehicle owners owed about $6.7 million in unpaid tolls dating back as much as five years. The bill now moves to the Senate.

Another bill that advanced Saturday in the House would ban the use of restraints on prison inmates who are more than four months pregnant. A final House vote is expected Monday.

Delegates, meanwhile, balked at a proposal to charge shoppers a nickel for each disposable bag they use. As originally introduced, the legislation would have created a statewide requirement. A revised bill sought to allow interested counties to impose the fee — something Montgomery already does.

On Saturday morning, one of the two House committees that considered the legislation voted it down. Among the concerns: having different standards in different counties.

Most major initiatives put forward by O’Malley (D) this session have either passed or are on track to pass. Bills to repeal the death penalty and provide incentives for an offshore wind farm have cleared both chambers.

And a bill cleared the House on Friday that would add about 13 to 20 cents per gallon to the cost of gas to help replenish the state transportation fund. Senate leaders have pledged to take up a gas tax bill before the session ends.

Still languishing is a gun-control package put forward by O’Malley. The legislation passed the Senate last month but has been stalled in committees in the House.

One House committee is weighing proposals to significantly weaken O’Malley’s proposed assault-weapons ban, potentially excluding some semiautomatic rifles favored by sportsmen and veterans.

Dozens of gun rights advocates greeted delegates Saturday morning as they arrived for their floor session. Others packed the House galleries. Because of a policy that doesn’t allow signs in the State House, some scrawled “2014” — the next election year — across their palms and waved to delegates.

Among the other late-moving bills is one that would allow illegal immigrants statewide to obtain Maryland driver’s licenses.

The Senate could vote on the bill as early as Monday. On Saturday, the House delayed consideration of the measure until next week.

The legislation would require Maryland to establish a second-class driver’s license, which applicants could obtain without a Social Security number or proof of lawful status, though they would still have to pass written and road exams, as do other drivers.

Immigrants would have to show some form of identification, such as a birth certificate or passport. Senators added a requirement that applicants also provide two years of state income tax filings.

Some 275,000 illegal immigrants live in Maryland, according to a recent study. Another 400,000 live in jurisdictions that border Maryland, including the District and Virginia.

Four other states have similar policies on driver’s licenses.

Kate Havard contributed to this story.