@AndyCr15 no you're right - there's also a heavy hormonal influence on it, and dietary considerations.. i.e. certain dietary choices based your insulin response will have a significant impact. i.e. someone who has little / low insulin resistance will have a different response to exercise and glycogen adaptation to someone that doesn't. In addition weight training does improve insulin response (i.e. improves insulin sensitivity) via glycogenesis cycle - but this are small cuts, but enough small cuts end up in having an impact if you add them all together with the other elements of dietary regulation as well as lifestyle adaptation - all the things you're doing are having that compounded impact.
However, your body adapts, it likes the path of least resistance, which is why it's always good to review every few months to see if the impact is still helping.
As for your weight loss, you're probably cycling more than lifting in terms of time under exercsion and cycling isn't always steady state, you will have to go up hills, accelerate decelerate etc, so it's a bit more dynamic. That said, cycling + some good weight lifting programmes are ideal. I've been doing a lot of swimming (easier on my poor knees that get punished through 2.5x bodyweight squats!
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Do you need weights to lose weight? No not at all. Is it advisable? Yes - not only for bone strengthening, but the hormonal response and building muscle tissue which ultimately helps to increase your metabolic capacity. However it isn't needed at all. See it as a catalyst, or a synergistic activity to go along side a good diet. Diet is key, as is sleep and lifestyle choices.
A sedentary big guy who is not doing anything other than living, may well burn similar calories to the whippet that is super active - but it does depend on numerous factors, and the sedentary guy will get to a stage where their muscle mass will drop to a point where their testosterone drops and therefore their oestrogen rises which makes them less anabolic = less muscle retained and therefore metabolic rate will lower despite their size. I'm eating around 3.3-3.5k calories daily, and I'm not losing / gaining weight, but I walk for 30+ minutes every day, and train 4x week and swim twice a week, I'm also relatively muscle dense and relatively lean (for my age and height) so I'm naturally burning a lot of calories just by existing.