Unless you give carrots or beetroot as greens but stick to the more leafy types with perhaps the odd bit of broccoli etc, it’s unlikely that a bun would get fat from greens. It’s pellets and treats that makes buns fat, as a rule. (Too much cabbage-family greens can potentially lower the metabolic rate because they have an effect on the thyroid).
If the bun you’re getting is adult and in good health, I’d suggest you try and encourage hay-eating as much as you can. If he/she eats hay, he won’t get malnourished and you can use pellets more or less as a supplement. If it’s a baby bun, he’ll need pellets ad lib until he/she is 6 months +, unless he/she is a total pig, and perhaps also alfalfa hay.
A big rabbit is a bit tricky to weigh on a kitchen scale, but it is really helpful to weigh a bun every month or so (and write down the weight, because it’s easy to forget). That way you’ll know if your bun’s diet is ok. It is really hard to see if your bun looses or gains weight. You tend to just wake up one day to a very fat rabbit, and that’s not fun for either of you. (Happened to me with my Bam. He gained 300 grams (10,5 oz) on the sly and had to be put on a diet.)