I wouldn't bother with the Baby Bjorn. We bought this for our first (also 9kg at 15weeks) and though I think it was ok then, it didn't last him long thereafter - by 5.5 months his bottom just sank down all the way onto the floor so it didn't work as a bouncer, and became only a rather expensive seat which was uncomfortable for a big boy.
However, what has worked well second time round, with our even bigger and heavier DS2, is the Fisherprice newborn to toddler chair. This is a bouncy chair with several recline positions, a toy bar over it, and a vibrating function. Being larger to accommodate a toddler size it was very comfy for DS2 to snooze in and he would happily watch us from it.
Re jumperoos, our DS was over the weight limit for his before he could use it properly, although he did get enjoyment from it nevertheless. Door bouncers didn't work for us at all - again DS was too big and heavy, the harness was too small to support his body and he just sank all the way down to the floor unable to bounce.
You will also need to think about moving up car seats if you haven't already as your DS is likely to outgrow his group 0 seat before he is ready to go forward facing - there is lots of info on mumsnet and elsewhere about extended rearward facing. When DS2 outgrew his maxi cosi cabriolet at 5.5 months we bought a Hauck Variogard seat which has been excellent, some of the other extended rearward facing are aimed at older babies who can sit properly whereas the Hauck has a supportive shell.