Welcom to the site, Jordan. Your question is an excellent one. Firstly, let me say that we definitely do not regard a 25kg GT as "small". A fish of that size is an excellent fish and an achievement to land. Of course, GTs do grown much larger than that and there is little doubt that the 100kg monsters are out there.
The reality though is that while there are a lot of fish in the 15-20kg size bracket out there, there are lesser number of larger fish and fish over 50kg, while not rare, are certainly more uncommon. I often use the terminology "you don't grow that big if you're stupid" and I think it is very appropriate for big GTs. Small GTs will often do quite suicidal things but larger fish tend to be more cautious in their behaviour. From my experience, I have noted that many of the larger fish tend to be more ambush hunters. That is not to say that big fish are not aggressive - I've seen them do crazy things when the feeding instinct is on but it is rarer to see this behaviour.
I know there is a school of thought, particularly in Hawaii, that the larger fish tend to inhabit deeper waters. I don't have a firm view on this as I don't have the knowledge but I have noticed an inordinate number of big fish are captured jigging. One of the largest fish I have captured myself was taken on a jig at a depth of not much less than 100m.
I don't have the experience in your area but if you have 15 - 25kg fish, I see no reason why there would not be the odd fish that is a lot larger than that around. I'll ask you the question of whether you've been busted off by any fish while popping that was unstoppable. If so, I would wager that was the odd larger fish.
In terms of targeting them specifically, I have not found a method that works effectively. I've tried using very big poppers but the reality is that GTs are very aggressive and I've seen 25kg fish attacking a 5kg live mack tuna meant for a dogtooth. About the only thing I can say is that if you persevere, you will undoubtedly hook the odd larger fish among the GTs. Whether you can land it or not is a different question!