Below are some books I know about. FYI, I read approximately the first half of a public library copy of Ferrar's book back in January or February of 1974 while enrolled in a 9th grade Algebra 1 course (however, in my independent reading/study of math I had completed the Algebra 2 material by this time), and I found it to be something I could understand and follow, which was definitely NOT the case with some college calculus texts I had seen at public libraries. I mention this because the book seems to be rarely mentioned on the internet, and thus will likely be overlooked by people looking for something like this. The other books, except for Brewster's book, are either well known or (because they're old enough to be in public domain) are in the process of becoming well known. Sawyer's book is not really a textbook, but I'm including it because I suspect it introduced a lot of "mathy types" in the 1960s and 1970s to calculus, as it was in the "New Mathematical Library" series of books that high school libraries back then often had several volumes from.
Calculus Made Easy by Silvanus P. Thompson (1910, 1914)
Calculus: An Intuitive and Physical Approach by Morris Kline (1967, 1977)
Calculus for Beginners by W. L. Ferrar (1967)
What is Calculus About? by W. W. Sawyer (1962).
Differential Calculus for Beginners by Alexander Knox (1884)
Elementary Illustrations of the Differential and Integral Calculus by Augustus De Morgan (1832, 1899)
Commonsense of the Calculus by George William Brewster (1923)
(ADDED NEXT DAY)
I can't believe I overlooked Calculus in Context below. I don't remember how I learned about it, but I've had a copy of the 1995 hardback edition since 1995 or 1996. I've used some of the material in classes (for example, Section 12.1: Stirling's Formula on pp. 690-699 and Bessel’s Equation on pp. 564-573 in classes here during the late 1990s), and I often used to flip through this book for ideas about how to introduce certain topics in class (such as Section 3.6: The Chain Rule on pp. 138-147). There’s a bit of computer program stuff in the book that’s probably out of date now, and there's some material on discrete dynamical systems topics that was avant garde in the late 1980s to late 1990s, but I was never much interested in this material and my interest in the book was for its exposition and its inclusion of certain topics that you rarely see in standard calculus texts. I’m almost certain I’ve written about this book on the internet, but for some reason I can’t find anything nontrivial now.
Even better, this book is now (legally) freely available on the internet, although if you find you really like it, then you'll probably want to get a print copy. The book (1995 edition; I haven't seen a print copy of the 2008 edition) opens nicely and the font size is medium to large (I'd guess either 12 point or 13 point), which makes it very easy to use.
Calculus in Context. The Five College Calculus Project by James Callahan, et al. (1995, 2008)