To get a sense of the scales involved in high field magnets, take a look at this page
These nearly 2 T (20kG) electromagnets weigh 500 - 1500 lbs, depending on the size of the sample volume, and require a large power supply and chiller. The weight comes partly from the heavy copper coils (blue in the pictures) and otherwise from the massive iron cores and yokes needed to convey flux without complete saturation. The 2T figure is not arbitrary--it is the saturation induction of iron. Moving higher requires other approaches.
The ultrahigh field magnet lab magnets that you referred use multiple stages of nested superconducting windings, typically without ferromagnetic cores. The sample volumes are generally very small at the highest fields.