Size has disadvantages, as well as advantages. Human weapons of the same basic form came in a variety of weights, and smiths would regularly resize swords, the way rings are resized today. A small but very strong human could wield a zweihander that was fitted to his strength, and for the same reasons a huge human would wield a zweihander--and the huge man might be at a disadvantage, since his bulk may make such a large weapon slower and more easily avoided, while offering a larger, unshielded target.
Strength, skill, and the purpose the weapon was being put to, were atleast as important as the size of the fighter using it.
A very small being might favor an axe, for the same reasons a woodsman uses an axe to fell a tree--quick blows, smoothness of operation, and deep penetration into even bone. Picks and the like offer even deeper penetration, at the risk of losing your weapon to the wound--and against a single titanic foe, a deep wound to a vulnerable area may be worth a dozen scratches. Spears, as well, make sense against large warriors, for the same reasons they make sense against large prey--again offering penetration, as well as reach and accuracy.
Swords work well for those of similar size, where size isn't the deciding factor, and where many blows may be traded before one or the other opponent is laid low.
Giants and ogres, on the other hand, might favor broad maces or flails, as even a glancing blow can crush a small, fast, hard to target being, and where penetrating power is a disadvantage, instead of an advantage. An uprooted thorn tree seems like a crude weapon, but that doesn't make it ineffective. Swords and axes aren't that valuable against very tiny foes, and could be replaced with cheaper and/or more effective weaponry. A trident would work far better than a spear, for a giant, offering all of the advantages, and few disadvantages.
A giant would rarely ever seek to throw a weapon, other than a rock or a stick--well made gigantic weapons being exponentially more expensive, and more than exponentially difficult to make. Bronze would probably be favored over iron, and even steel. The added weight and hardness won't mean much, and the corrosion resistance would be invaluable. Bows would be ridiculous in the hands of giants, except against ships, where a single arrow might sink a galleon.
Simple discuses, on the other hand, could break masts, smash walls and towers, and be used to slaughter whole phalanx at a time, from both short and long range. Far more effective in the hands of a gigantic being, than in a normal human.