Why is uranium's atomic weight listed as 238.02891, higher than almost all known isotopes?

The isotope mass of uranium-238 is 238.05078826 amu, which is greater than 238. So it's not surprising that the standard atomic mass (averaged over relative abundances of all isotopes) is greater than 238 amu as well.

In fact, the masses of most heavy nuclei are greater than 1 amu per nucleon. This is because the binding energy per nucleon is lower for larger nuclei, and so the mass defect is smaller.

Note that both the mass of a bare proton and a bare neutron are slightly greater than 1 amu (1.0073 amu and 1.0087 amu respectively), and the masses displayed in isotope tables include the masses of the electrons as well (0.00055 amu). So the only reason that any nuclides have a mass below 1 amu per nucleon is because they are more tightly bound and their mass defect is correspondingly larger.