The suffix -some, like previously-mentioned -ful, has an applicable sense. From etymonline:
word-forming element used in making adjectives from nouns or adjectives (and sometimes verbs) and meaning "tending to; causing; to a considerable degree," from Old English -sum, identical with som (see some).
Words with this kind of -some suffix include handsome, winsome, toothsome, wearisome, etc. (Words with the other two -some senses that etymonline.com shows include twosome for sense (2), “suffix added to numerals meaning "a group of (that number),"” and ribosome for sense (3), “word-forming element meaning "the body," Modern Latin, from Greek soma "the body"”.)
For the latter part of your question – opposites of unitless and dimensionless – note that dimensional has among its senses “Having dimension or dimensions”, and the word has been frequently used in the phrase dimensional analysis, which refers to the process of analyzing dimensional units of quantities. But dimensional analysis works with unitless quantities as well as dimensioned quantities, so dimensional is not quite satisfactory as an antonym for dimensionless.
Dimensionful (“(mathematics) Possessing dimension
”), on the other hand, while it sounds like a neologism and dimensioned seems to me more appropriate, is nevertheless in regular use as an antonym; eg:
In such a case, we know that the ordinary Klein-Gordon action does not require any dimensionful prefactor, for J d²cr(daÛ)² is indeed dimensionless when the Klein-Gordon field Û is itself dimensionless.
[In the quote, I substituted Û for X-hat]