Stalin did offer peace in 1941 and 1942, at least in some point with terms returning to the pre-Winter War borders. But Finland refused, because at this point there was still the possibility Germany wins the war and in the end a separate peace would have made Finland worse off in the aftermath. There also were the German troops in Finland, in Norway and already by late 1941 in Estonia. The Finnish army in 1942 would have been in deep trouble with the circa 200 000 German soldiers that were within Finnish borders and could have ordered reinforcements and air support at will, at least in comparison to the Finns.
Geopolitically, in 1941-42 Finland was dependent on Germany or in the USSR's mercy. For war materiel as well as food. Without German food shipments, Finland would have seen famine in these years due to failed harvests and severed trade connections to the rest of the world. As long as Germany was strong enough to hold its own on the Eastern Front, it could starve the Finnish people and raze most of Finland to the ground if Finland stepped out of the line. Realistically, the only military help against the German troops inside Finland would come from the Red Army. And allowing Soviet troops freely roam on Finnish soil was, to the people who had lived through the Winter War, tantamount to national suicide.
Changing sides in 1942 would mean having the Finnish interior become a part of the Eastern Front overnight. Not much of an option to any sane leadership, I'm afraid.