Because Finland is militarily nothing compared to Russia.

In other words, countries with such weak military power will not benefit NATO.

Hi! Greetings from Finland!
I'd like to correct a couple of things in your post. Despite being a small country of about 6 million people, Finland actually has a very strong army. This is because we have been preparing for the enemy's attack for about 80 years. Back then there was The Winter War when Stalin tried to take Finland and failed.

Today, the Finnish army is modern and strong. We have the biggest artillery in western Europe. We have more tanks than Germany for example. We have 64 F-18 fighter jets and just bought 64 F-35s. We were the first European country to buy JASSM cruise missiles in 2012.
In our country military service is mandatory. Our troops are well trained and motivated. We can mobilize 300.000 soldiers to the eastern border within weeks. According to American military studies, Helsinki, the capital of Finland would be one of the most difficult cities to occupy in the world. This is mainly because of the deep, vast tunnel system in the bedrock under Helsinki. This was created for war.

Right now Russia is having huge difficulties in Ukraine. Finland with a much more modernized army than Ukraine would be a lot harder to take.

Finland is a very desired partner in the perspective of NATO and especially the USA. Our military budget is way above the NATO standards already and unlike many other NATO countries. As NATO partners, Finland and Sweden would also defend the Baltic airspace because we have our own fighter jets. This is big deal for NATO. They will benefit massively for us joining the alliance.