Selected answers from the Dumb SEO Questions G+ community.
Casey Markee: Splitting authority and efforts among multiple sites or properties is seldom, if ever, a sound decision. I would urge you to keep everything under one domain when at all possible.
Not only is this a better use of resources, time and costs but there are clear ranking and user benefits to keeping everything together.
Francois-Pierre Marcil: Management agility vs. pure SEO? SEO wise, what Casey Markee said. But, you should never undervalue the advantages of being agile from a business point of view. Ultimately, it depends on what stage your business is at. If you are a startup with an unproven product or service, agility is probably more valuable as you want to prove that your offering can work first. That being said, if you are a startup selling watches (or a more mature business) and there is nothing new with your offering (beyond the quality of your product), then you should care about the SEO aspects a lot more.
Alan Bleiweiss: Given that both Casey and Francois-Pierre have valid points worthy of consideration, it`s important to emphasize that what this comes down to is you need to balance all of your business goals and needs, where SEO is one consideration. How much weight you give to SEO as one of several considerations is up to you in your unique situation.
David Harry: I am going with my standard answer these days; it depends
Ammon Johns: Does the blog directly contribute to the success or satisfaction of the average visitor journey to the shop? If so, of course they belong together. If not, well, precisely what is the purpose to the blog? When you then factor in issues about the brand, and whether the blog is an integral factor of their brand, or is something done mostly for SEO and actually makes their brand look like a follower rather than a leader, you start to get a better picture of where it belongs, and whether it is something to make a core part of the shopping site, or something to keep at arms length, if not further.