Finland fought three distinct wars in WW2. First, the Winter War, in 1939-1940, against the Soviet Union. At this time, Germany was allied with the Soviet Union. Second, the Continuation War, when Finland fought against the Soviet Union as an ally (but officially a "co-belligerent" rather than an ally). Third, the Lapland War, against Germany (with some fighting also in the Baltic, with the Lapland War opening with the (unsuccessful) German amphibious invasion of Suursaari). Once, they were fighting against an alliance that included Germany (but without fighting Germany) ("the friend of my enemy is not my friend"), once fighting alongside Germany ("the enemy of my enemy is my friend"), and once fighting against Germany ("the enemy of my enemy is also my enemy if they can force me to fight them").
However, it was just a convenient coincidence that Germany attacked the Soviet Union and Finland took advantage of it. The stance of "co-belligerent, not ally" was propaganda, and there was significant pre-planning and cooperation.
Historically, Finland had been quite pro-German since independence (which was in 1917, after the falls of the Tsarist government and its replacement, the Provision government). Finland's independence was promptly followed by civil war between Whites and Reds, with the Whites winning with German support. The Whites, who now controlled the Finnish parliament planned to make Finland a constitutional monarchy, and elected a German prince to become the King of Finland (Friedrich Karl Ludwig Konstantin Prinz und Landgraf von Hessen-Kassel, brother-in-law of Kaiser Wilhelm II). The monarchist plan evaporated with Germany's defeat in WW1, which made German royalty rather less attractive politically. Frederick Charles abdicated before coronation (and before going to Finland), and Finland became a republic.
Finland's 3 main neighbours: Germany (across the Baltic), Sweden, and the Soviet Union. Sweden was a "safe" neighbour, and Finland sought friendly relations and military alliance. Sweden preferred a stance of neutrality and disarmament (but also friendly relations). In the later inter-war period, the Soviet Union opposed military cooperation between Finland and Sweden. Sweden was a safe neighbour, but the prospects of being a useful neighbour in a major crisis dd not appear good. Finland's post-independence relations with the Soviet Union had not been good. The Russian Empire's program for the Russification of Finland (since 1899) were deeply unpopular in Finland, and contributed to the declaration of independence. The defeat of the Reds and the departure of radical Red Finns to the Soviet Union didn't help. Neither did Finnish intervention in the Russian Civil War in Russian Karelia and in the civil war in Estonia. The Soviet Union was seen as a neighbour to be feared more than trusted (and Finland's defence spending was higher than that of Sweden or Norway, largely as a result of this).
Germany was a possible major local power that could help against Soviet pressure. Alas for Finland, the Ribbentrop Pact made Nazi Germany and the Soviet Union officially friends and partners in crime and the carving up of the parts of Europe unfortunate enough to be between them. With the invasion of Finland by the Soviet Union in 1939 (the Winter War), Germany demonstrated its commitment to the shared project with the Soviet Union by blocking military aid shipments (from other countries) to Finland. (Finland was not unfriendly to the whole Axis - Italy offered and tried to send military supplies).
With defeat in the Winter War, and a very wary relationship with the Soviet Union, Finland saw German conquest of Denmark and Norway, largely isolation Sweden and Finland from neighbours other than Germany and the Soviet Union. Then, the defeat of France. Isolation! Finland (and Sweden) had to tread carefully! The Soviet takeover of the Baltic States (Estonia, Latvia, Lithuania) showed what wrong steps could lead to. German conquest of Denmark and Norway, hardly rivals or enemies of Germany, showed that Germany could be predatory too.
Then came increased trade with Germany. German shipment of military supplies through Finland (to northern Norway). Arms supplies from Germany. German plans to invade Arctic Russia through Finland (from Norway), and ideally Finnish participation. Finland could strongly contribute to Germany's war aims by cutting the Murmansk railway, by keeping Soviet forces busy in Russian Karelia, and by attacking Leningrad.
Could Finland have said "No"? If Germany defeated the Soviet Union, and Finland had not helped, the eastern end of the Baltic could become a quite unfriendly place.
What would the benefits to Finland be? As noted above, if Germany won, being on the winning side would be politically useful in the post-war world. In addition, there was:
The recovery of territory lost in the Winter War. Many Finns approved of this.
The possibility of a Greater Finland incorporating part of Russian Karelia. Some Finns approved of this; many felt this was wrong (consider the scene in the famous Finnish war novel/film, Tuntematon Sotilas, where the Finnish soldiers consider the morality of crossing the pre-Winter War border (of course, this is a post-war work, and post-war thoughts might intrude)).
What would the cost be to Finland? Apart from the human and economic costs of the war, there was the obvious risk of Germany losing. Finland took 3 steps to reduce the impact in case of such a loss:
The Finnish government pushed the idea that they were not allies of Germany, but "co-belligerents" who happened to the fighting the same enemy.
Finland halted the drive east which would have cut off the Murmansk railroad, in response to US pressure (the US demand was to stop fighting and return behind the pre-Winter War border; in the event, not cutting the railway was sufficient to satisfy).
Finland refused to attack Leningrad; their advance was past the pre-Winter War border, but was halted about 30km from the city centre. The Finns refused an explicit German request to attack Leningrad.
Also, Finland largely halted offensive operations at the end of 1941.
In the end, the Continuation War ended with peace terms that could have been much worse, and it is likely that these steps contributed (also, the Soviet Union being still busy fighting Germany).
For further reading:
The main English-language study of the Finnish-German alliance/co-belligrency: Henrik Lunde, Finland’s War of Choice: The Troubled German-Finnish Alliance in World War II, Casemate, 2011.
There is more on German-Finnish cooperation and planning before the Continuation War/Barbarossa in: Lars Westerlund, The Finnish SS-Volunteers and Atrocities against Jews, Civilians and Prisoners of War in Ukraine and the Caucasus Region 1941–1943, The National Archives of Finland and Finnish Literature Society (SKS), 2019: https://www.arkisto.fi/uploads/Julkaisut/sarjajulkaisut/SS-VOLUNTEERS_verkkoon.pdf