I know lots of people that have been trying to lose weight for years - they show up at the gym everyday to do low-intensity cardio and they never lose any weight. It's generally because of what they're doing on the nutrition side.
If additional weight contributes to injury, then it is easier to put more effort into nutrition to get the weight down before working on the exercise front to decrease injury potential. Then you can get the two working in parallel.
4 x IG Prestige MP, 70 cm, 376 grams, 386 SW, ALU Power @50