Is there an enjoyable way to do it that isn’t just about 20x reps here, 40x reps there?
That isn't really weight training - it sounds like Bodypump, which will tone muscles, but isn't really calorie-burning resistance training. Real weight training (or at least what weight trainers call weight lifting!) is going pretty heavy and low reps.
And I love it!
I do 2 sessions a week with a PT - the first 30 minutes is strength training: either deadlifts, or squats, or sled push. It makes you really strong and also lean. I have steel abs, without really doing much targeted core work, because you're using your abs to brace in squats, for example, or doing pull ups or push ups.
I do Bodypump classes because they're fun, but they're fairy weights because there are so many reps. When I'm heading for, say a deadlifting personal best, I'm just thinking about 1 rep. But it's 97 kilos (I'm heading for 100 kg). I'm in my early 60s, and I'm the fittest & strongest I've ever been, and currently on a progressive overload - I've gone from just managing 90kilos deadlift before Christmas, to multiple reps at 95kilos. And so on.
Weightlifting also helps me run faster. But I'd much rather lift up heavy shit, than run!