To the Stamp Act's credit, the whole purpose of it is right there in the first line:

An act for granting and applying certain stamp duties, and other duties, in the British colonies and plantations in America, towards further defraying the expences [sic] of defending, protecting, and securing the same. (1.1)

It's not like they were pretending or anything.

France and Britain were the two big kids of Europe at the time, and had spent most of history hating each other's guts. The Seven Years War was really just the latest in a long history of war stretching back to a time before "France" or "Britain" as we understand them even existed. The difference with this conflict was that the war stretched all over the globe.

And that can get expensive fast. Think about how much it costs to ship things. Now imagine it's 250 years ago, and a lot of modern stuff you take for granted doesn't exist. Anything that had to cross an ocean had to do it in a rickety boat pushed by wind. That's right: a stiff breeze was the highest technological advancement for travel speed the world had.

So it was expensive and time consuming. France was a powerful enemy too, and was well entrenched in Canada and the Ohio River Valley. They had good alliances with local Native American nations. Any victory was going to be costly.

Parliament wrote the Stamp Act specifically because of the war. They wanted to pay for it, and keep troops around so that if either the French or Native Americans started anything else, Britain would be ready.