The way it stands right now, large size is an advantage in 5E. If you take an NPC and change him from medium to large you give him more HPs and double his weapon damage. Any disadvantage for being large is inconsequential, and that's especially true when you realize that being small has disadvantages as well and small characters don't have nice perks like +1d4 damage (or double weapon damage if you go by monster size advantages). The lowest CR for a large humaniod is CR2 (The Ogre). The weakest of the 'giants' should be able to take on an entire party of level 2 players. Give that orge class skills and a better armor and weapon selection and he would start with an even higher CR.
It would be nice if there were pros and cons for characters based on their size, but that's not how 5E was built. If your player made the same exact barbarian as a halfling and a large sized half-giant then the damage potential differences would be huge. If the halfling was suddenly a large race in your game, then it would become the best weapon fighter based just on the perks of size.
I like the idea someone had earlier to make large races be a mandatory 2 to 5 level class choice (based on the racial features you want). That way if one player starts as a large sized half giant then the other players would be level 2 to 5 in their class. A halfling barbarian would have a second attack at 5th level and the large race barbarian would need to be a higher level before he gets to have two attacks. I also think this would avoid the whole 'watered down' approach that WotC is using to try to get playable minotaurs and other races that should be large.
I would just try to avoid having a race that is optimized towards certain classes in such a way that any other racial choice would be unwise.