I'm looking for a suffix that has the opposite meaning of the suffix -less as in stainless. That is, a suffix that means “not free of ...”. In German, for example, there is the adverb “behaftet” and one can say “fehlerbehaftet” (meaning “not free of defects”).
In particular, I'm looking for opposites of unitless and dimensionless (w.r.t. physical quantities).
There is no universal affix in English equivalent to the German suffix behaftet.
Instead, there are two different ways to form this kind of adjective in English.
The suffix -ful suggests that the noun modified has the quality in question in abundance. It is a limited suffix that can be used only with certain words: hopeful, but not hungerful.
The past participle of some verbs can also be used as an adjective. For example, the opposite of "stainless" is "stained." Again, this does not work with all verbs, and I'm not sure what the rule is. It seems to be more common with transitive verbs ("stained," "baked") but also includes some intransitive verbs ("fallen," "wilted"). It cannot be used with nouns, but is often used with words that share a noun and verb--all four of the examples above fall into this category, and it may in fact be a requirement.
Your specific examples don't fall into either category. They're both nouns, so the verb tense trick doesn't work. ("Dimensioned" is a word but suggests "having been dimensioned" rather than "having a dimension.") And neither is on the -ful list.
So you have to use a multi-word construction instead of a suffix. This is pretty common in translating from German, which, from a native English speaker's perspective, seems to have an affix for just about everything.
Without commenting on the more general forming of anti -less terms, you could consider unitized and dimensional.
The -ful suffix can frequently be used to form the opposite of an adjective ending in -less.
Another general translation of the behaftet concept might be -bearing. That would be appended to form a hyphenated word, e.g. a fruit-bearing tree. Note that a fruit-bearing tree is not quite the same as a fruitful tree. The former emphasizes the general behaviour of the species, while the latter emphasizes the productivity of one particular tree. (In German, fruchttragend and fruchtbar, respectively.)
As another example, the opposite of being blameless is to bear blame. It could be expressed as a hyphenated adjective blame-bearing, but in practice, such usage is rare in English.
A unit-bearing number would be a good way to express the opposite of a dimensionless quantity, and in my opinion, easier to understand than "dimensioned", "dimensional", or "unitized". That said, I have difficulty finding examples of such usage in the wild… here's one.
To translate fehlerbehaftet, I'd simply say defective, faulty, or imperfect. Since those simple expressions exist, anything else would be awkward.
The above answers are indicative of existing usage and contain a lot of good ideas. However, here's another one.
Especially in technical jargon, people invent words like "unitful" or "dimensionful" and they often stick. For example, "stateless objects" in object-oriented software design are objects that don't carry state between method calls. "Stateful objects", meaning "objects that are not stateless" are objects that do carry state between method calls. These words were invented back in the 90's, and they caught on because they are a concise, intuitive, and accurate way of describing the phenomena to which they allude.
So, if perhaps you were writing an article about "unitless somethingorothers", you might state that you were going to use the term "unitful" to mean the opposite of "unitless" in the paper. If it's a useful enough word (and it seems pretty clear that its meaning is easily grasped intuitively, difficult to mistake, and more economical than most of the alternatives), it could very well catch on. So why not? Shakespeare did it. :)
And I would consider dimensioned as an antonym of "dimensionless." In that I disagree with the learned @chapka.
Consider "fraught" as another suffix antonymic to "less."
As well as the previously-mentioned hyphenated affix -bearing, consider also the possibilities iferous (e.g. carboniferous, odoriferous), -laden (e.g. guilt-laden, dust-laden, bin-laden) and -carrying (e.g. load-carrying, knife-carrying).
These won't work universally, but may be useful now and again.
In my experience reading and writing in nuclear and particle physics, dimensionful is the clearest and most common antonym for dimensionless. Some quick searching reveals many examples from the arxiv, such as this recent abstract which explicitly uses "dimensionless and dimensionful" as antonyms.
The suffix -some, like previously-mentioned -ful, has an applicable sense. From etymonline:
-some (1)
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]
