Jeff harbored a deep-seated resentment against his father. The XYZ Foundation bases its decisions on a set of deep-seated beliefs. Carol’s deep-seated sense of loyalty convinced her to stay despite grossly unfavorable conditions.
The phrasal adjective “deep-seated” is another one of those English idioms that can be a source of confusion, even among native speakers. In particular, some people may be inclined to use “deep-seeded” instead. And that would be incorrect, even if it almost makes perfect logical sense.
In effect, you can think of something as being deep-seated for one (or more) of three primary reasons: the thing has existed for a very long time, the thing is very difficult to change, or the thing is rooted at a very profound level. Many religions have deep-seated beliefs, for instance, that have been a part of the literature for centuries. People hold these beliefs very strongly, deep in their hearts.
When you consider “deep-seeded” as the alternative, the literal understanding seems to fit the bill too. If you take a seed and you plant it deep into the soil, you have literally seeded the ground deeply. This kind of imagery aligns with the notion that a belief, a tradition, or a resentment is deep and difficult to change or uproot. But it’s still wrong.
The “seat” refers to placing one thing deeply into something else. It can also refer to a location where something is concentrated or centered upon. The heart is the seat of passion. King’s Landing is the seat of power in Westeros. In this way, beliefs that are deep-seated are buried deep within a person’s worldview or understanding.
English is a fickle language. Idioms like “a hair’s breadth” can look strange, particularly because words like “breadth” are not normally a part of casual, everyday speech. The same is true with this use of “seated.” Thankfully, a quick Google search will usually point you in the right direction and, hopefully, that direction is at one of these Grammar 101 posts.