The Company took little gear of war, for their hope was in secrecy not in battle.
Fellowship of the Ring Book II Chapter 3: "The Ring Goes South"
Aragorn, Boromir, Legolas, Gimli, and Gandalf all had equipment they trusted, and which they were accustomed to tramping through the Wild with; they didn't really require anything else.
It would have been challenging to equip the hobbits in Elvish gear; the time required to make four suits of Elvish mail in hobbit-size probably would have been prohibitive, and would have looked very unusual to any spies of Sauron or Saruman.
But the hobbits weren't completely defenseless; they still had their barrow-blades:
The younger hobbits wore the swords that they had taken from the barrow;
Fellowship of the Ring Book II Chapter 3: "The Ring Goes South"
The elves probably could have given them Elvish knives, but why bother? Blades of Westernesse do the job well enough1.
Finally, Elrond did furnish them with some useful things; N_Soong has already mentioned the miruvor, but he also gave them some items of more mundane utility:
All were well furnished by Elrond with thick warm clothes, and they had jackets and cloaks lined with fur. Spare food and clothes and blankets and other needs were laden on a pony, none other than the poor beast that they had brought from Bree.
Fellowship of the Ring Book II Chapter 3: "The Ring Goes South"
The last factor to consider is weight; every item the Fellowship took with them had to be carried, in theory,all the way to Mordor; a trip that took five months for Frodo and Sam alone. Every pound is precious in that situation.
1 Obviously Sam could have used a little extra help against Shelob, but it's questionable whether Elrond could have forseen that, or if he could have provided anything even if he had. Even Sting wasn't enough to kill Shelob, or even harm her signficantly; she was only defeated because she speared herself on it