The verb ‘to attenuate’ means ‘to make (something) weaker’ or ‘to reduce the force of (something)’. The concept of attenuation has various technical interpretations in the fields of, e.g., physics, botany, and brewing, while the word attenuative has been applied by some grammarians to suffixes which serve to weaken or reduce the force of a word (see, e.g., Martin Maiden and Cecilia Robustelli, A Reference Grammar of Modern Italian (London, 2000), pp. 439-440). In English the suffix ‘-ish’, added to an adjective, sometimes has attenuative force – thus ‘reddish’ means ‘rather red’, ‘warmish’ ‘rather warm’, ‘tallish’ ‘rather tall’ – though the suffix ‘-ish’ has several other uses besides its attenuative use. In Italian the suffix –astro, added to an adjective, has a similar use: e.g., verdastro (greenish), dolciastro (rather sweet) - though the suffix –astro (like ‘-ish’ in English) also has other uses.
The Oxford Dictionary of English Grammar (Bas Aarts, Sylvia Chalker, & Edmund Weiner eds., 2nd ed., 2014) lists the term Downtoner, which it defines (p. 220, sub Intensifier) in a way that makes its meaning virtually identical with that of attenuative.