In the interview, this is what was said:

Q: How will the Zodiac Weapon story develop in the future? What's its position in Heavensward?

A: Up to now, players have worked very hard on the Zodiac Weapon story, therefore we do want to avoid saying, "okay please forget everything you did". In Heavensward, because the character level cap is being raised, adventurers would be able to experience further growth themselves, and we would like players to aim at going through new content and obtaining different items. Now, whether it will be the "Zodiac Weapon story", or whether it will be a successor, we plan to start the game of grow-your-weapon in 3.1 again.

Q: When that happens, are the owners of Zodiac Weapons getting some considerations?

A: Yes, of course.

Q: But before that, in 2.51 the Zodiac Weapon gets another power up.

A: In 2.51 if you complete the ultimate form of the Zodiac Weapon, this will remain your strongest weapon until Heavensward is released, so people should be able to find a lot of use for it.

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TL;DR:

Yoshida specifically avoided concluding whether the ZW itself will end or whether it will be continued, but there will be content like the ZW quests in 3.1. People who own the ZW can expect some benefit (though no mention of what form) when that time comes. And lastly the ultimate form of ZW in 2.51 will be the best weapon in the game until 3.0 release.