Modern high efficiency furnaces must flow significantly volumes of air over the heat exchanger to draw down the exhaust to condensing temps. Many of them have safety mechanisms that will prevent operation if they can't achieve enough flow, however, depending on the type of safety mechanism, it may allow intermittent operation until the EGT's hit a limiter.. I would expect the return duct on a 60K BTU condensing furnace with short runs would need to be about 1 square foot of cross section in total... If that's split out to multiple registers, that's fine, but they need to branch out to something that adds up to around that same amount of cross section or more, and the registers themselves, which act as a point of restriction, should have more cross section than the ducts... For example, if you have a 6" round duct for a return, it should probably interface with a 4X10 grate.
While the house may have insulation problems and leaks, it's also possible that you're not even getting a fraction of the heat possible out of that furnace because it is being staved of air and only operating the burner intermittently.
Ideally speaking a ducting system for a modern furnace should have enough registers/ducts that the air velocity through the registers around the house is actually pretty low, but adds up to lots of flow with minimal restriction.
If you think you're pretty solid on finding and sealing up leaks... the next point to hit, as others have stressed, is certainly attic and the top of walls. It's common for insulation to have settled down the walls, leaving the top corners in bad shape, which is where all the heat goes, so is where the insulation is needed most. It's also common over the years in a home for previous homeowners to dishevel or remove attic insulation for various reasons, especially if animals or bugs turned it into a nesting situation. Try to make sure that all surfaces in the attic over living spaces have at least ~8". Modern code calls for more in your zone/region, but if money is tight just get what you can up there. Blown/loose-fill products of various types can be install by hand. Wear a good mask, maybe respirator, headlamp, and be very careful where you step, making sure to keep your weight on the trusses. A few hundred bucks worth of loose fill would probably get things off to a good start.