There's no specific height or weight specified, but you definitely get bigger. The size change language includes:
If you lack the room to become Large, your size doesn't change.
Even if common English definitions of relative sizes didn't apply, this would still imply that you in fact get physically larger (if you didn't, you wouldn't need the extra space). Aside from that it's up to the DM; if I were in charge, I'd just make you the size of some common humanoid Large creature (e.g. an ogre), but there's no fixed size specified, so anything reasonable works.