LYNN – Kathy Atkinson likes riding the commuter rail into Boston so much she refers to her fellow riders as “the train family.”But Atkinson also said there is room for improvement aboa-rd the trains: She wants the Massachusetts Bay Transportation Authority to hold off cutting weekend service to save money in the face of its budget problems.”I worry about the loss of weekend service on the economy if people don’t go into Boston,” she said.The MBTA has threatened to cut train and bus service to balance its books but it says commuter rail service remains prompt and reliable.MBTA spokesman Joe Pesaturo said commuter trains, including ones running through Lynn between Boston, Ipswich and Rockport, have logged a 94-percent on-time arrival record for the last three months.”This is the highest level of service in more than three years. Commuter rail has been performing at an exceptionally high level of service,” Pesaturo said.Lisa Flammia said she never has problems with late trains but said the MBTA needs to adjust train schedules to accommodate workers who do not work 9 a.m. to 5 p.m. schedules or work during the evening or on weekends.Pesaturo said the MBTA has improved on-time performance by improving train and rail signal maintenance despite the money problems the agency faces.Rising gas prices are funneling record numbers of riders to the MBTA’s fleet of buses, subway cars, commuter trains and ferries. Fare collections are expected to grow by $4.5 million in the coming fiscal year.Sales taxes are the agency’s largest single cash source and a drop in tax revenue leaves the T with less money to pay for equipment maintenance and to pay off its debt. About 30 cents of every dollar of new revenue, including fares, will go into debt payments.Without new revenue sources, MBTA General Manager Daniel Grabauskas has warned the agency will have to raise fares and cut back on services just as it is hoping to lock in a new generation of riders. The T has already raised fares three times – more than 75 percent – during the last eight years.