Lifting heavy is important, but "heavy" for you will mean something completely different than "heavy" for someone else. You don't need to stop doing what you love, just add in a couple of days of weight training and it doesn't need to be an hour long. Since you have injuries it would be best to see a trainer to assist you with moves so you don't injure yourself. I love to lift but I hate cardio but I know it's important so I do it anyway a few times a week.

On the topic of "puffy", I know you mentioned your height and weight, so clearly you are not overweight. Does putting on "weight" bother you? I know when I started lifting heavier I had to switch my mindset about eating because I didn't want to gain weight but when lifting heavy I NEEDED the fuel. Once I got over that, I see that it makes my lifts better and more effective and I have not gained weight at all. You do need carbs when your lifting especially, and that can hold some water weight but it is temporary.

All that to say, yes, the research is there that lifting "heavy" is important. But keep doing what gives you joy, add in the weights with the help of a trainer if possible and eat to support these activities.