The.Bard said:
Initially, I thought the feeling seemed to be: "How dare you give me ME2 for free when I wanted something else!"
Nothing is free, especially when there's a corporation involved:
1) They get free, positive press and image polish on any gaming site out there (and incur positive opinion from people like you going "arrr, those ingrates, it be free but they not be pleased!")
2) They get people using the EA Download Manager, an in-house sales platform / Setting up an Account and everything if they haven't already, Portal wasn't free but was a Promotion to get more people to use Steam, same thing with Alien Swarm.
3) They hope to increase Dragon Age 2 sales by offering a "package deal", something is inherently not free it it is bound to another product, it is an "extra".
4) They hope to get people that have gotten Dragon Age 2 (or haven't gotten it yet but are about to, see #3) to look into the Mass Effect series and increase their customer base that way, also generating extra press and word-of-mouth for their release of Mass Effect 3 in a few months.
5) They hope to sell DLC, they offered the "base package" bundled with Dragon Age 2 (which can be gotten for mere 10$/10pound by now) e.g. it has lost a lot of its initial value, but they are still selling their DLC which people starting the game now might be inclined to buy.
I'm sure there's more, but those should be a start.