If Google suspects that your site has been buying links, yes, your site will be severely punished in the rankings. Read about how American retailer hired an SEO company to get it good rankings and it did so using a bunch of low quality links on low quality sites and how Google retaliated.
If done incorrectly yes. Influencer marketing is basically link buying. However, the links are no follow and an FTC disclosure must be used. If you are purchasing do follow links you will be punished by Google. But, if your goal is to drive awareness and traffic with no follow links you won't be punished.
Weak backlinks are from spammy sites with little authority links coming in. That is how JC Penny's SEO consultant did it, with thousands of links from low-quality blogs nobody reads.
thinking about buying huge links on low-quality blogs may harm your value website. we should always be focused on high quality and thematic link setup for better performance.