What effect does the suffix -ly have upon word stress?
The usual answer is none. This suffix has no stress of its own. It leaves unchanged the stress of the stem to which it is attached.
From ˈhappy we form ˈhappily, from proˈfound we form proˈfoundly, from ˈaverage we form ˈaveragely, from ˌsureˈfooted we form ˌsureˈfootedly.
But there are occasional exceptions, at least for some speakers. We all pronounce ˈnecessary with initial stress. Some of us have a weak and compressible vowel in the suffix, thus ˈnesəs(ə)ri, while others have a strong one, thus ˈnesəseri etc. In the latter case you may say that the suffix has secondary stress, but I don’t think there are any mainstream speakers of BrE and AmE who place the primary stress on the suffix. (Caribbean English may be another story.) Yet for the adverb necessarily we see that many Brits and probably all Americans shift the stress from nec- to -ar-. (Personally, I belong to the presumably shrinking proportion of Brits who don’t do this, but feel it more natural to keep initial stress and a weak -ar- in necessarily ˈnesəsrəli.)
The same applies to other -ly adverbs formed from adjectives in -ary, as voluntarily, primarily, arbitrarily. It can also apply to those from at least some adjectives in -ory, as articulatorily, obligatorily, though not apparently perˈfunctorily. Now I have heard another exception: a TV commentator talking about resoˈlutely opposing something or other. Presumably, like the rest of us, he would stress the unsuffixed adjective on its first syllable, ˈresolute. So why wouldn’t he say ˈresolutely?
I don’t know how many other speakers would agree in having this stress alternation, or what other adjective-adverb pairs there might be for such speakers that follow the same irregular pattern.