Although the coupling are the current favourites to win, some fans of the show are predicting it won't last for long.
Some have even accused Curtis of playing the biggest game in the villa.
"Like am I the only one who isnt fooled by Curtis!? Hes fake as f***!" one Love Island viewer tweeted after the latest episode.
Another agreed: "He wants to be THE couple the one who's together from the beginning 'mum and dads of the villa' hes the biggest game player in there."
A third shared: "I think Curtis is so dodgy. Get the feeling that he's a massive game player #LoveIsland"
"Curtis is faking it with Amy, big time game player #loveisland," claimed a fourth.
Meanwhile, appearing on Love Island spin-off Aftersun, comedian Joel Dommett suggested that Amy and Curtis wouldn't make it to the end as a couple.
"I do really like them because they don’t just care for each other, they care for other people," he told Caroline Flack before adding: "But, sorry to say it, I think he is going to stray eventually.
"They are like Laura and Wes last year who were so nice early on and so amazing but three weeks later...
“It’s a long time. Someone is going to come in and he’s going to have a chat with someone.”
Despite the doubts from outside the villa, inside Curtis and Amy appear to be going from strength to strength.
In last night's episode the pair couldn't seem to keep their hands off each other as they took themselves away from the other Islanders.
They continued to grow closer before a rather messy snog.
Amy told the beach hut: “Lesson learned. Don’t wear red lipstick in the villa while you’re…well he’s not my boyfriend, while you’re in a coupling!”
And a teaser for tonight's (Tuesday, June 11) episode revealed that the pair were the first to enjoy a night of privacy in the hideaway.
Love Island 2019 continues nightly on ITV2 at 9PM.