I am thinking of building a broodmaster character who will go around with combat maids with each wielding between one to four weapons but if the attack limit also limits the number of weapons that can be wielded such a build will be impossible.
A traditional eidolon is only limited in its natural attacks …
indicates the maximum number of natural attacks that the eidolon is allowed to possess at the given level. If the eidolon is at its maximum, it cannot take evolutions that grant additional natural attacks. This does not include attacks made with weapons.
(Emphasis mine.) Thus a traditional summoner's eidolon can be handed a greatsword so that it can use its base attack bonus (therefore its iterative attacks) to cut down the summoner's enemies and do some simultaneous biting or tail slapping or whatever with its natural attacks as secondary natural attacks and the summoner needn't fear that he's breaking the rules by having the eidolon swing a sword. (This is fortunate as the archetype broodmaster is exclusively for the traditional summoner.)
…But an unchained eidolon is limited by total attacks
indicates the maximum number of attacks that the eidolon is allowed to possess at the given level. If the eidolon is at its maximum, it cannot take evolutions that grant additional attacks. Attacks made with weapons, including those granted by a high base attack bonus, are counted against this maximum.
(Emphasis mine.) So, yeah, this combined with the way the columns are set up can leave a full-attacking weapon-wielding unchained eidolon unable to make its iterative attacks from its base attack bonus if it would rather make natural weapon attacks. This is an unusual exception to the normal rules for the interaction between a creature's base attack bonus and its natural attacks.