Prometheus made a healthy profit. The budget for the next one can be higher because of this. Also they added "Alien" to the title, thus giving it brand recognition and possibly adding hundreds of millions to their box office. Finally, Australia not only stretched their money, but they offered a huge rebate for filming there. Thus, you can say that Covenant had a budget of $200 million or $150 million and both are, in a sense, correct. Same thing happened with Exodus: they spent $200 million, but got some back and ended up with a "final" budget of $150 million or so.
There really is no mystery to this and I'm amused to see so many people doubting that Covenant could cost $200 million. Logan is Fox's big tent-pole movie for next summer, and Prometheus outgrossed X-Men: First Class. This could literally be the studio's biggest release of the year, and it's actually a safe bet, economically. Since Fox lost Star Wars to Disney and Fantastic Four is an aborted franchise, they just have Avatar, X-Men/Wolverine, and Alien, now. Avatar has been postponed many times, and they are ending the Wolverine franchise, and they had mixed success starting a new X-men series with Apocalypse, so I can easily imagine them betting the farm on Ridley Scott's next Alien film.