Especially in large/huge map with a lot of civ, city state are the way to go both in term of expansion and military strategy. Perhaps they have trouble by themselves to conquer city, but with a little help they can go a long way.
During my last game (prince/Earth map/Huge/12 Civ/28 city states), I manage to take the lead in science, and every time I have a surplus of unit (especially after a war) I would send at least 50% of my army to a city state in need. The units take time to arrive, but when they do they shift the balance of power toward the city state (thus me in the process).
In that game, Hanoi conquers 3 cities plus the capital of the ottoman, Bucharest 3 city to Ramesses II, all of this without me having to declare war since they were under attack. On the North America continent (I was in Europe personally) I armed the 4 city states and they wipe out the US and Germany (which was lagging in term of tech) plus take 2 city to the Iroquois. In that case CS did all the heavy lifting. All I add to do was to become allies with the CS, send my unit that I had built for another war that just ended (upgrading them if necessary) & send three carrier and a navy to protect them, and 4-5 scoot to find the target to bomb. If you take into consideration the money save from unit maintenance and the resource free, its a pretty cheap way to take care of 2-3 civ on the other side of the world.
So city states are much more useful that only been your food supply. They give the possibility to bother a great deal enemy (especially the aggressive one) without having to be in a direct conflict. And since it easy and rapid to build an army in case you come under attack and with the maintenance cost in Civ 5, there is actually no reason to keep a huge army in standby. So why not give it away to someone in need? Personally, on the long term, building unit or upgrading old one just to send them to city states is worth it.
Worth case scenario the city state get kill, too bad but your maintenance cost is down, freeing resource each turn that can be affected elsewhere. If they dont capture a city, you have an enemy IA that is block in a war it cannot win, which will crush its treasury and shift its focus on something else, like attacking you or developing itself toward its victory goal. And sure best case scenario, the CS defend itself and go on the offensive, and put out of the race for good another major CIV.
Thus, city states are probably the best way to control the balance of power, in particularly in large map. Especially since sending unit as a gift is not public information, no-one, including the aggressive Civ is going to blame you. So does it make you feel powerful? Hell yes! Been able to take down a bad guy and been seen as the good guy in the process feel damn good! It is like been the US during the cold war or the British Empire, messing with the situation in continental Europe so that no one can compete with its powerful navy.
And best for last, one the CS has conquered a couple of city and armed, they can become powerful allies when you go to war, especially since they open a second front on the other side of your enemy. And there is nothing worse than having to defend yourself when you realize that you are being attack on your back side.