The eidolon totally gets iterative attacks with a manufactured weapon when its base attack bonus is +6 or higher. From here...
Base Attack Bonus (BAB): Each creature has a base attack bonus and it represents its skill in combat. As a character gains levels or Hit Dice, his base attack bonus improves. When a creature's base attack bonus reaches +6, +11, or +16, he receives an additional attack in combat when he takes a full-attack action (which is one type of full-round action—see Combat).
Base Attack Bonus: A base attack bonus is an attack roll bonus derived from character class and level or creature type and Hit Dice (or combination's thereof). Base attack bonuses increase at different rates for different character classes and creature types. A second attack is gained when a base attack bonus reaches +6, a third with a base attack bonus of +11 or higher, and a fourth with a base attack bonus of +16 or higher. Base attack bonuses gained from different sources, such as when a character is a multiclass character, stack.
Undoubtedly there are edge cases wherein a creature using a manufactured weapons doesn't get iterative attacks, but such a feature would be noted among the creature's abilities.
Natural weapons for the most part don't yield iterative attacks. Instead, the creature uses one natural weapon during a standard attack, or all its natural weapons on a full attack, with some natural weapons designated primary and other natural weapons designated secondary as per this chart; secondary natural weapon attacks suffer a -5 penalty to attack rolls and the damage bonus from the creature's Strength score is halved.
A creature wielding a manufactured weapon that also possesses natural weapons who takes the full attack action attacks with his manufactured weapon normally (including iterative attacks due to base attack bonus and usual damage bonus due to Strength) and can also make natural weapon attacks with any natural weapons not occupied with the manufactured weapon, but all such natural weapon attacks are considered secondary, suffering a -5 penalty to attack rolls and the damage bonus from the creature's Strength score is halved.
A cursory search should reveal questions probing the use of natural weapons in Pathfinder and its precursors and get answers that go into staggering detail.