So sorry to hear that you are losing a family member. It's not an easy choice to make and so hard to know when the "right time" is.
I just went through this two weeks ago with my 13.5 year old kitty. He was diagnosed with stomach cancer in june and lost so much weight since then. In the end, he was under 7 pounds as well and in his prime he was a 16 lb cat.
I, too, didn't know what to do. My husband kept saying he was getting worse, but I was so hopeful and in denial that I didn't see it all. I finally made an appt with our vet for a check-up to see if he was suffering, in pain, dehydrated, etc. Deep down, I knew it would be his last visit. I sent our son to a friend's house (he's only 20 months), took photos of my beloved furry friend and then loaded him up for the vet.
She was nice enough to tell me what he was going through, but also what they could to do help if I wasn't ready to let him go. Well, I realized it's really not my choice to keep him just because I want to spend more time with him. He deserved the chance to go peacefully before it was too much for him and to go after such a nice day. His last one was a very good one that he was still able to enjoy.
My husband arrived at the vet during the visit and let me take the lead on what we should do. After bantering a bit, I understood that the time was right at that moment. It was one of the hardest things I've ever done. But I like to think it was one of the kindest, too. I was there, stroking his head and giving him kisses to the very end. Our vet was wonderful through it all, too.
It's so hard to let go and I understand your husband's reluctance. I'm still grieving over my loss but have finally come to peace with the fact I didn't wait until he was truly suffering, but instead set him free with dignity. Perhaps a simple "well kitty" visit with your vet could change his thinking as mine did.
One other thing, I just saw a posting recently from a vet assistant on putting pets to sleep that said she wished everyone would stay with their pet until the end, even if it's hard, because they look for you when you leave the room. They've given us so much that we owe it to them to hold their paw through to their next journey.
I hope your family finds joy in the memories.