I was apprehensive telling dh as I wasn't too sure how he would initially respond, but I knew he would be ok after a discussion so never actually told him until I had ordered, it had arrived and I was sure I was ready to start (about a week after it arrived as I changed my own mind about 100 times after it arrived). 🙈
Fortunately the media hype/scare reports on weight loss injections never registered with him as it is not the kind of thing he is interested in (it's not cars, lobster fishing or football 🙈) so he didn't have any pre conceived ideas about them.
He was concerned that it was an injection and not via a "proper" Dr, but when I laid out very honestly and emotionally how I felt about my obesity, the issues I already had, where my future health was heading, and my inability to control my obsessive eating (including fessing up about what I ate when he wasn't around) he was a bit shocked, saying he just didn't realise just how much it was impacting me. He still a bit concerned about the medication but at the same time said he trusted me, he knows I am risk adverse and the type to do all my homework. I also discussed with him how important it was to me it was kept private and he respected that. We haven't really discussed it much since, 11 months on it is just normal I inject once a week, just like I take my multivitamins every day.
He said if I am eating healthier he will take the opportunity and do it too and he has lost a couple of stone and is enjoying the amount of protein - especially the steaks! - we have now instead of endless pasta and rice! Maybe that will convince yours to get on board too?
If your dh won't listen to you (you need to listen to his concerns too) and respect your request for privacy, that is simply not acceptable and you need to talk it out, perhaps over a few days, be honest about your feelings and struggles, no-one goes on these injections just for fun, and see where you end up.