Where can I find the dimensions and weight of a game?
Check with Board Game Geek.  On pages for games, they have a list of all versions with the size and weight.  For example, see this entry for Race for the Galaxy.  It states that pretty much all versions are 10.83 x 7.48 x 2.56 inches and 1.44 lbs.  Other games should also have version sections with similar information.