Several years ago I remember being able to walk into toy shops and
actually shovel lego bricks into a bag and thus buy them in bulk.
Official LEGO retail stores offer a similar service called Pick-A-Brick, which is available online and in stores. Despite having the same name, they each have their own differences:
The LEGO retail outlets house a matrix of bins, each filled with a certain type of brick. The bricks used tend be excess bricks from LEGO's own factories and some bricks of the same kind may be included in more than one bin. Bricks are packed into small or large plastic cups, you pay for getting as many bricks as you can in one cup.
The online version of Pick-A-Brick allows you to choose between thousands of individual pieces and colours. Parts are sold by the brick, each with their own prices with an additional fee for postage, packaging and handling involved.
Then there are also the LEGOLAND stores which aren't classified as LEGO stores (despite The Lego Group having a large chunk in the theme park company). These too offer a similar Pick-A-Brick service, with a larger range of parts then the average LEGO retail store. Since the stores are located inside the park you must pay admission to the park to browse the shop.1
Unfortunately I can't seem to find stores anymore that offer this
There are many unofficial stores dedicated to selling LEGO.2 It's possible that some of these independent stores would offer their own service which typically sells bricks by weight.
1. Incidentally, I had contacted the Legoland Windsor representatives in 2010 to see if it's possible to visit the store without paying admission. 'You will need to purchase a full day ticket on arrival but as long as you return to guest services within 30 minutes these will be fully refunded'.
2. I haven't come across any independent LEGO stores living in England but I've seen a few in Eastern European counties.