The development of the Space Shuttle (STS) and the Hubble Space Telescope (HST) were running in parallel during the 1970s and 1980s. Both plans for STS and HST were announced in the late 1960 and both used each other for justification.
HST faced some major financial problems throughout the years for various reasons. One recurring enabler for cost cutting was the Shuttle's alleged ability to bring HST back to Earth to fix problems. This argument was for example used to reduce the number of in-orbit replaceable items/instruments, cut down on testing, etc. See e.g. Robert W. Smith, "The Space Telescope. A study of NASA, science, technology, and politics" for an in-depth description of this part of HST's history.
In the end, they realized that if you wanted to bring back HST back to Earth, you'd need to have a processing facility where the HST could be received, worked on, and prepared for relaunch. Having such a facility on stand-by throughout the envisioned life time of HST was determined to be prohibitively expensive and the whole idea was scrapped. HST's final design considered in-orbit repairs only.
HST was over 11000 kg and contained highly sensitive instruments and a giant mirror. If I recall correctly, it barely fitted inside the payload bay.
From this answer the biggest item brought back by STS was LDEF, which weighed about 9700 kg and was basically a stainless steel passive structure. The other satellites STS brought back were considerably smaller and lighter than HST.
Was the Space Shuttle actually capable of bringing HST back to Earth? More precisely, given that both were designed around the same time, are there requirements for STS's design (that made it into the final design) that account for the required ability to bring HST back?