Which professional could do this job in my bathroom?

You need a experienced tiler, or a multi trade builder. However a floating floor would likely be the route I'd go down apposed to filling a large void with concrete.

I agree with the above. Filling the empty space below the floor will affect the breathability potentially of the property and could lead to damp issues. A suspended floor is more than capable of carrying tiles (upstairs bathroom for example) as long as the floor is well supported and the span not too great. If the joists are of a long length and you are worried about bounce in the floor, perhaps a brick pier wall installed onto the ground under the floor with gaps in to allow for air circulation could be the answer to support the joists mid span. As for tiling this is done on a decoupling mat to allow for any expansion in the floor surface. Extra noggins may be enough to lessen the bounce if only slight however. I hope this helps.

Hiya ive come across this on rare occassions where extensions have been built without proper regs being done, rife in the 80's when everyone was a "builder" Im assuming the floor has flex in it from your description of it being very "weak" As mentioned above i would not suggest filling with concrete because there is more work/cost and potential issues with that route than it is worth. You may need to replace or double up the joists depending on what is there and the span of the room or possibly build brick piers underneath but again that will need some sort of foundation to build off. It is likely the way forward is to put bigger joists next to the original and then fix your floor to these. This will remove the flex but even then it is still recommended to use a decoupling system as mentioned above along with a flexible adhesive. This will need a competent builder who is aware of the need to prepare for a tiled floor. Then of course a bathroom fitter to do the rest

A competent builder would be able to do this for you. In my opinion, I would recommend a solid fill - especially for a ground floor bathroom. Anything else may allow for small amounts of movement and could lead to leaks.