I want to know why this is. Scottish people aren't short and hairy, as far as I know. Why not French dwarves? Why not Irish dwarves? Why not German dwarves? Certainly if Dwarves have to be hopped up on testosterone, German will work just as well as Scottish. It's almost as cold.
I am given to understand that Scotsmen do not make a habit of living underground, marrying women with beards, or subsisting mainly on beer and gold (as does the stereotypical Dwarf). I may, of course, be wrong, but be suspicious of anyone from the Southern part of the Isle agreeing with this portrayal.
How did this start, and how can it be changed?
Change it? Well, that's not really up to the writers, that's up to the movie directors.
Personally, I have an issue with every "foreign" person in a movie having a stilted British accent. Take "Troy" for instance -- if Brad Pitt had really spoken in a thick Greek accent with all its gutteral aitches, he wouldn't have been half as sexy. "Ever After" was set in France, but just about everybody spouted the King's English.
My friends and I have decided to call this default Hollywood accent "foreign."
Dwarves must just be from the mountains in the North of Foreign.
On the other hand, you know how the English feel about the Scots...
I always think it's weird that Romans have highly cultivated British accents. What's up with that?
The whole British accent thing is another cliche. Happily, it's one that I actually dig. 
As I understand it, when the Celts migrated to the Isles, they pushed the people who were already there (the Picts) to the north and west. Then the Saxons (Vikings) came and pushed the Celts further north and west, which pushed the Picts even further.
Some believe that the small size of the Picts, along with an ability to disappear into the wild easily, was the basis for the idea of the magical "little people."
So that gives you Scotland, to the north, where the "little people" survived the longest.
The Celts were not "little people" (cf. Chesterton's "Great Gaels of Ireland"), but the Picts were.
The people we think of as Scots now are Celts, by the way.
We all love cliche's anyway, so why change a good thing that we can't get "enough" of?
"It's not the size o' the hammer that counts, it's how you wield it."
Which seems to stereotypically sum up their being good with mining implements, possessing a somewhat risque sense of humor, and the aforementioned accent/language issue. So it's not just literature and film...the expansive video game industry is propagating the stereotype(s) as well.
Inkwell
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"The difference between a writer and someone who says they want to write is merely the width of a postage stamp."
-Anonymous
I read recently an book by the producer and head honcho of "Everybody Loves Raymond," Phil Rosenthal. While casting, he says that the network vetoed him casting other ethnic Italian New Yorkers to play the family of Ray Romano (actor) / Ray Barone (character), despite Romano being New York / Italian. Apparently the network suits thought it wouldn't play in Middle America if it were too ethnic. The end resulted in a funny-but-not-necessarily-believable mixed-ethnicity family. On a glance, it's hard to believe these people are related to each other. (A more thorough look lends more credence to the idea---they certainly behave towards each other like a family. I didn't appreciate the show as much when it was on but have found it lately growing on me.)
I think this kind of "ethnic neutering" plays across the entertainment media. Ethnic types that can't easily be pinned down as to place-of-origin get cast in parts like, say, the abovementioned dwarves. If the traditional Scotthsh stereotypes are played down, in this modern era, who would know except us suspicious and observant types?
(Noted in passing: "dwarves" is Tolkien's spelling---it was normally "dwarfs" before The Hobbit.)
And surely you all know that dwarves are smiths!