“The health of the citizens of Pennsylvania is worth more than the profits desired by health insurance companies,” Rose Lynd, 35, of Pittsburgh, testified at a hearing in Harrisburg held late last month by the Pennsylvania insurance commissioner, Teresa D. Miller, a former Obama administration official.

Ms. Lynd, a cancer survivor, said her costs were onerous.

“My premiums are more than $600 a month, which is more than our mortgage payment,” Ms. Lynd said. “I am grateful that the Affordable Care Act is here for my family, but I am disappointed by its limitations. All I want is a plan that makes our health care affordable, but it doesn’t exist.”

Highmark defended its request by saying it was paying out more in claims than it was receiving in premiums. Jeff Scheib, the vice president in charge of actuarial services at Highmark, offered a statistic to illustrate the problem.

“There were close to 250 individual A.C.A. policyholders in Pennsylvania who incurred over $100,000 each in claims and then canceled coverage before the end of the year,” Mr. Scheib testified. “This behavior drives up the cost to insure the entire pool, because people use insurance benefits and then discontinue paying for coverage once their individual health care needs have been temporarily met.”

While state insurance commissioners, who review rates, are trying to balance the needs of consumers and insurers in a turbulent market, insurers have extra leverage this year. At least a dozen nonprofit health insurance cooperatives have collapsed, and several big commercial insurers have decided to cut their losses by limiting their participation in the insurance exchanges, the new marketplaces created under the health law.