You're a good person and it sounds like he is too, regardless of his insecurity here. But, and this is important, it is crucial to be able to talk about these things straight up and honestly (which can still be civil, friendly, and nice of course, but "honestly" means "not beating around the bush" and direct).
In ANY good relationship there will be conflict at some point. That is not negotiable and the idea of a conflict free relationship is fantasy, a fairy tale myth. What matters is not that there is NO conflict (again, this is impossible), but how it is handled and resolved: that both people are actually open and honest about what's really going on under the surface, insecurities, etc. This can lead to some pretty difficult conversations and awkward moments, but it ultimately leads to a much tighter relationship in the end.
He needs to know that his constant harping on it and his attitude are is really bothering you (not like distraught or anything, but that it really actually bothers you). That it makes you feel bad. And he needs to be told that this powerlifting thing is a part of who you are, and it is important to you, and that you feel like he hates that you do it and that bothers you. He also needs to know that it is non-negotiable that you train less, because again this is part of who you are not just a random interest.
As difficult as it may be, he also needs to hear your statement you made about the gym being your "dream date" environment, in a team sense, and that you want to have fun with him instead of feeling tension there. His back injury is probably is directly related to the fact that he is trying to keep up with you and he wasn't prepared for the weights he was attempting, but that's not something you have to say to him lol.
I think those concerns he voiced to you have a strong insecurity as the cause of them. He is undoubtedly sincerely concerned for you, but he is also almost certainly voicing those as a way to subtly stop you from lifting because he is insecure. I doubt he is actually aware of that motive though, so don't tell him that! lol. It is very likely to be subconscious. He can't believe that you are better at something or can handle (physically) something he can't. However, he needs to learn that it's ok to have somebody be better at something than you.
You can verbally validate his concerns for your health ("I don't want you to hurt your back while deadlifting", etc) by telling him you are glad he is concerned and wants you to be healthy, and you can do this while making it clear in no uncertain terms that stopping deadlifting and squatting and arched benching is not negotiable because again the love for powerlifting is a core part of who you are as a person.
Bottom line, all relationships have conflict and any that don't are hiding it or about to have a blow-up down the road. He needs to know you feel hurt by his words and actions, and that you love the sport.
As an aside, I really recommend the book "Keep Your Love On" by Danny Silk. It talks a lot about the concepts of conflict and emotional validation in relationship and though it has the most obvious carryover to romantic or family relationships the principles are useful in all relationships--business, school, friends, etc. It is definitely a book written from a spiritual perspective (Danny Silk is a Christian pastor), so if you're uncomfortable with references to those things you may have a little trouble with the book. However, I have found that the book is extraordinarily helpful regardless of whether one is a Christian or even religious at all, as long as one can accept examples from religious life being used. I highly recommend it regardless of your beliefs but wanted to throw it out there so that you didn't get surprised. It's short, and not preachy at all, it's not trying to convert anybody or anything.
Hope something I said helps.