The UK is the only one's who have ever invested on infrastructure. And it is all mostly to support the fishing industry. This is about money for the UK. The people who live there are descendants from people of all sort of places, because they were fishermen for a British fishing company. No wonder when asked, they prefer to be considered British. All Argentina has ever done on the island is bombing them.

Proximity matters but only up to a point. The Islands aren't that close to Argentina, I can't remember what the exact limit is but under international law islands along to the country whose coastline is closest to them up to a distance of 10 nautical miles as long as there is no claim already in place. Of course that's an international treaty which historically didn't necessarily count, which is why you've got things like American Samoa and Hawaii.

The US is closer to Greenland than Denmark is.