You can find weapons everywhere in FF7. You can either find them in dungeons, acquire them rom battles or just buy them in weapon stores across various cities and towns.
Weapons have attributes, attack power and materia slots. Some of these slots are single slots while others are double slots. Double slots make it possible to combine 2 materia orbs, for example, 'all materia' together with 'ice' results in 'ice-all'.

These will give the character extra attributes, such as immunities or strength. Unfortunately, no materia slots in these.