I haven't flown Fiji, but some general thoughts -
Once we started flying more non-US airlines that have more restrictive carryon limits, we made a point of getting suitable smaller and very light rollaboards for those trips. That way we have a better chance of them both looking ok - so they are less likely to look like something that should be weighed or measured - and actually being within weight limits or at least reasonably close, in case someone does check. It depends a lot on the airline and situation, and in reality it hasn't turned out to be an issue too many times. In general, I'd say flying business is likely to let you get away with more. But while it's good to check what a certain airline is likely to do at a certain airport, the trouble is you can't 100% count on it so you have to be prepared, somehow. Also, you may find they don't care too much on US departure, especially if it's a codeshare or a US airline is handing ground logistics for a foreign carrier. But they might care on the return. (We ran into that going to Australia, I believe that was the experience that inspired us to get new rollaboards.)
I also recommend getting over the desire to carry on too much stuff - losing stuff is not actually that likely, and the introduction of new tracking technologies over the years has made it even less likely than it used to be (but the worry lives on.) Regs are an issue at least in the Philippines, they don't allow them in carryone for some time now, don't know if there are other places like that. Paying attention to how you book your flights, having flights on one itinerary and adequate layover time as much as possible, is always a good idea. Getting certain places a day early is a good idea. Make sure all your bags have full itineraries to help something lost or delayed to catch up with you, it can't hurt.
Another thing we've noticed with foreign airlines that have low carry-on limits - while not universal, some seem to give more of a crap on average about your checked luggage than the US carriers. Maybe it's cultural, maybe they've been forced to since they're not letting people carry on so much, I dunno. But maybe that balances things out a little.