This term, always used in a derogatory sense, can mean one of two things. I'm going to suggest here that both usages are incorrect.
The first, most common usage these days is "you don't support the team when they're down." The second, more common when I started watching sports (20-odd years ago), is "you're a fan of whichever team is winning."
Now, on the face of it, these are both silly insults. They strike me as more appropriate to a civil war than sports fandom. If I switch sides in a war to whoever's winning/pays me more, than I have no conscience; if I desert my side when they're losing, I have no courage. Those are character flaws worth noting when you asses my worth as a friend or compatriot (however, pointing out people's character flaws to change them usually only works in movies.)
Where's the character flaw in caring less about a sports team than others, or caring for a different team when it suits you? This is entertainment. It's like criticizing someone for liking or not liking a particular movie or piece of music. Those likes and dislikes can, and often do, give you a good start on getting to know if a person is someone you'd enjoy talking to or be bored by. But they have nothing to do with a person's conscience, courage, or any other virtue. There are people whose interest in a team waxes and wanes, or that only enjoy watching the winners, who are generous and kind. There are die-hard fans of every team on the planet who are complete jerks.
As for me, I suppose I'm "fair-weather" category 1. The Trail Blazers, like any professional sports team, regard me as a customer whose only value is the money that can be earned from my fandom. Accordingly, I regard the Trail Blazers as a business selling a product, and if that product is not entertaining, I have no obligation to buy it. However, I grew up in Portland, caught BlazerMania during the Drexler years, and so I can't imagine the kind of happiness I've felt when the Blazers were doing well being transferrable to another basketball team. When Drexler went to Houston, I enjoyed watching him win a title; if the Blazers had been contenders at that time, I would have rooted for them over the Rockets. Now when the Blazers are lousy, I simply pay less attention to basketball altogether. (I don't think I watched a single playoff game this year, except if it was on TV at a bar.) Life's full of entertainment (too much so, perhaps?) and there are many other ways to pass my time.
If you plan to follow every game of a sub-par Blazer team, interested in observing the development of the coaching staff and the young players . . . good for you! I'm glad you take joy in that. (I'm glad whenever people enjoy something that doesn't involve cruelty to others.) If I run into you or read something you write, I look forward to hearing your assessment of the team's progress.
I'll admit, I tend to be bored by most "fair-weather" category 2 people. At least when they talk about sports. On other subjects, they may be erudite, but when it comes to sports, their interest seems to be displaying that they have the know-how to pick a winner. Picking a winner when someone's winning isn't an especially fascinating trait. Now, if someone picks a winner when they're losing and knew before most everyone else why that team would surprise us all, that's intriguing to hear.
Even so, if you always root for the champion . . . good for you! Again, it's a harmless hobby, and I'm happy you have one. I just don't want to hear about it. You don't want to hear me go off about different beer yeasts, most likely. Let's talk about something else.
When anyone starts slinging around the supposed insult, "fair-weather fan," however, I am not just bored. I'm a little bit disappointed. It's belittling others because of their hobby, for crying out loud. To me, that shows an intention to demean somebody else in order to boost one's own self-esteem. This can be therapeutic when castigating a person for immoral behavior (speaking with friends about mean exes, or lambasting a crooked public figure), but when it comes to harmless hobbies, it's a sign of stunted emotional maturity.
If a teenager likes listening to a pop star whose music makes me want to Van Gogh myself, that says nothing about the teenager. Does the music say something about the pop star? Quite possibly -- and I enjoy talking about that sort of thing with friends, our likes and dislikes. But I would never demean that teenager for her/his taste in music. I did when I was 14. I grew beyond it well before the time I started enjoying Blazer basketball. Blazer fans, fans of any sport, should stop using "fair-weather fan" as an insult; it demeans the speaker more than it does the recipient.
On the other hand, the song "Fair Weather Fan" by The Baseball Project is kinda cool. Unless you're a complete poseur.