Google's algorithm is not known to us so we are left to guess. There could be some case studies but even so, the algorithm changes around 500 times per year so it is impossible to know for sure.
My best guess is, all forms of attention grabbing on a page such as bold and italics are put in a bucket which share the weighting bonus. If you have only a couple words on a page appear in bold, then all the weight would apply to those couple words. If you present the entire page in bold, then all terms would be treated equally.
My normal recommendation would be to use bold for the most important words, or the most relevant ones. If you feel the design of the page improves by using bold text on the first couple of sentences, consider changing the text color instead. I have seen some creative results in this regard but don't have any examples to share.