Weight loss body vs bike

[Hell27]

Hi, I'm currently on a mission to shed a lot of weight as through injury, breaks in training, Christmas and beer festivals saw me go up to an awful 20st 1lb at Christmas. I've shed 1.5 stones, so am now 18st8lb, and it's getting better. My strava times are improving and I'm aiming for a target of 14st. In kg, I've shifted 9kg, and am aiming to shift another 28. That's the equivalent of 4 heavy road bikes! However, I was wondering if shedding weight on the body had exactly the same effect as shedding weight on the bike? My head is saying it should, but does anyone know differently?

[Hell27]

Thanks to all for the very informative replies, the notes of support are well received, thanks! Some others out there that have shifted large amounts of timber, well done!
I had quite a practical application of the difference in rotating weight this weekend. I was on a club ride, and picked up 2 x rear punctures. At the second, I got a bit pissed off with it and was ready to quit, then I examined the tyre and realised I had to quit! The tyre had picked up some glass or a thorn and put a big gash in the contact patch - no wonder it kept puncturing. So I put a new inner on, and nursed it 5 miles to the nearest halfords. I was running 35mm continental cyclocross speed tyres, lovely light, fast tyre, but obviously a little fragile. They weigh 350g each. So at Halfords I swopped them for a pair of 28mm schwalbe marathon plus. Great tread, very tough, but heavy. 750g per tyre, so 800g difference between the 2. It felt heavier after, but had a better rolling resistance. The ride was a lot worse, but I suspect I won't pick many punctures up. I'll keep them on for the time being for the commute, and see how they perform. I suppose the added weight can only help on the weight loss mission!