Here it means "according to," or "following the path of." Do what your faith tells you to do; don't rely on what you are seeing. Maybe definition 10 here: https://learnersdictionary.com/definition/by

In the phrase "walk by," there is a more "literal" meaning and the more figurative meaning. Literal: -to walk near or close to something, usually passing by it. For example: "Her house is the same street as mine. I walk by her house on the way to school." Figurative: -I believe I have only heard or read this expression used this way in a biblical context. It comes from 2 Corinthians 5:7 which says* "For we walk by faith, not by sight;" in this sense "walk" can be interpreted as "live" or "conduct oneself." To "walk by faith," therefore, is to live by faith. I agree with your comment paraphrasing it as "walk/live guided by faith/sight." My Spanish Bible is La Nueva Traducción Viviente and it translates it as "Vivimos por lo que creemos y no por lo que vemos." Biblically, "walk" is often used to mean "live" or "behave" or "conduct one's life." For example: Gen 5:23*: "Enoch walked with God..." Deut 8:6*: "Therefore you shall keep the commandments of the LORD your God, to walk in His ways and to fear Him." 1 John 1:6-7*: "If we say that we have fellowship with Him, and walk in darkness, we lie and do not practice the truth. But if we walk in the light as He is in the light, we have fellowship with one another, and the blood of Jesus Christ His Son cleanses us from all sin." *quotes above taken from NKJV Hope this helps!

Excellent, Carl. Your explanation was marvelous! Maybe I should interpret the expression "walking by sight/faith" as a shortened way of "walking GUIDED by sight/faith". What do you think about it? Thanks a lot.

Hi Jordi! Usually we need to see to walk or else you could run into a wall, or a pole. Literally, the quote is saying that you should walk without seeing, and just rely on your beliefs. However, the actual meaning is deeper. It uses walking as a metaphor for life, saying that instead of relying on what we see and have around us, we should focus on our beliefs and faith to guide us for life. As far as the meaning of walk by, it is referring to the way someone walks. I.e. if you were to see a bump, and avoid it you would be using your eyes to keep you safe (walking by sight). It is worth noting this is not a phrase that is normally used. In fact, I have never heard this spoken before, I've only read the phrase. DISCLAIMER: I am not a teacher, I am just a native speaker!