Carl,

I agree the UK was and remains a valued Ally, but it wasn't simply weighing the value of the relationship between Argentia and the UK, in that case the UK wins with a wide margin. The difficult part was assessing the potential on the region at large (Latin America). I think Haig did his job advising the President that it could cause problems. Reagan never waivered from supporting the UK, but admitted it put it us in a tough position.

It did result in severely undermining the Rio Treaty, but it was already problematic, so it wasn't that much of a loss. Furthermore, Argentia was an aggressive nation that concerned a lot of the nations in the region. Apparently they were getting ready to invade Chile before the conflict in the Falkands went bad (for them). In the end I don't think our low profile assistance hurt us.

http://www.gwu.edu/~nsarchiv/NSAEBB/NSAEBB374/

At a meeting in London on April 8, 1982, shortly after the war began, Prime Minister Margaret Thatcher expressed concern to U.S. Secretary of State Alexander Haig about President Ronald Reagan's recent public statements of impartiality. In response, according to a previously secret memorandum of the conversation, "The Secretary said that he was certain the Prime Minister knew where the President stood. We are not impartial."
a conversation with British officials at the end of March, Haig declared that the U.S. diplomatic effort "will of course, have a greater chance of influencing Argentine behavior if we appear to them not to favor one side or the other."
At the same time, the White House recognized that British intransigence would create problems for the U.S. in its dealings with Latin America. President Reagan, reacting to Haig's secret reports on the British position, wrote to the secretary: "[Your report] makes clear how difficult it will be to foster a compromise that gives Maggie enough to carry on and at the same time meets the test of 'equity' with our Latin neighbors."
More at the site.