While "jab" is used almost universally across UK print and broadcast media to describe an injection, it's interesting to note the choice of accompanying adjective.
The Sun, The Telegraph, Daily Mail and The Times love to use "fat jab".
The BBC, The Guardian and The Mirror seem to prefer "slimming jab" or "weight-loss jab".
It is just the usual vice vs. virtue approach to things where 'the right' tends to point at vices which are in need of curtailing while 'the left' points at the virtue in those turning away from such vices. This also relates closely to 'the right' tending to voice support for punishing those who commit vices in some way while 'the left' voices support for rewarding those who turn away from committing them. Deeper down it points down to the preference for personal agency and responsibility on 'the right' versus collective responsibility and a related lack of personal agency on 'the left'.
The Sun, The Telegraph, Daily Mail and The Times love to use "fat jab".
The BBC, The Guardian and The Mirror seem to prefer "slimming jab" or "weight-loss jab".
There's a lot to digest in those choices.