You can't have any sort of health system that applies moral judgements as a criteria for selecting who is prioritised for treatment.
That said it is fair to ensure that obese patients take all possible steps to alleviate their obesity or lose weight before they are accepted for treatment. That's not a moral judgement but sensible clinical practice.
Equally you cannot allocate treatment in terms of who is the most deserving.
Both of the above are subjective and a dangerous path to go down.
But you can make an objective judgement in terms of the efficacy of IVF and whether or not it merits funding. I understand all the mental health considerations and speak from a privileged position of never having had to struggle with infertility but objectively infertility is not going to kill you.
It might be a contributing factor to mental health but objectively speaking (and I understand this is a really hard thing for anyone who has had IVF or suffered from infertility to hear) wouldn't it be better to treat the mental health issue?
When someone feels that they will commit suicide if they can have xyz happen to them, surely that's indicative that they need some kind of healing, which IVF may not solve?