You only charge fate-points for aspect usage in the exclusively narratively focused editions of Fate (like Fate Core).
In Fate 2.0, the aspect denotes a core character trait, and thus is something that is always part of the character. Indeed, if the GM ever concocts a situation wherein he strips the character of the use of an aspect (perhaps in this case by drugging the character to reduce their strength) the character gains fate points. In this system, the Aspect represents a major, identifying, characteristic of a character. It's always on, and you only pay to get special mechanical benefits above the normal. You don't pay to win an arm-wrestling contest with an aspect in Strength of Heracles, heck, you probably don't even roll. If you were wrestling the Nemean Lion, however, and rolled too low for your wrestling skill, you would be able to check off an aspect in Strength of Heracles in order to do some mechanical stuff and effectively have rolled better. They paying only comes up in extraordinary situations and represents your ability to succeed at things related to the aspect above and beyond what you normally could because of narrative buy in. In 2.0, Aspects are the backbone of the character-focused system, while the checking off of aspects contributes to the narrative-focused part.
In the latest editions of Fate, there is no longer much of any 'character-focused' part to the system, which now is entirely narrative focused. Aspects are still called aspects and named and such in similar manner, because they evolved from thorough revision to the previously existing versions of Fate. It's important to remember that in Fate Core and FAE you don't buy parts of a character, you buy ways you are allowed to influence the story. Skills aren't about things your character has learned or can do so much as they are about what you, the player, can do to evolve situations in the game, as reflected by the action system's narrative categories. Aspects, similarly, aren't about traits your character has so much as they are about labels your character has only when it's convenient for the story. 'Convenient for the story' should not, of course, be confused with convenient for the characters-- compels are if anything more important than invocations in Fate 3.0 (used here to refer collectively to FAE and Fate Core). But these labels are only 'on' in scenes where they're being shown and if they wouldn't be fun for the story in a situation, you oughtn't compel them, according to the Fate Core rulebook (and this is good advice).
So in Fate 3.0, an aspect in Strength of Heracles doesn't get you a strong character. What it gets you is a character whose strength you are allowed to have scenes showcasing. Because what you buy in 3.0 is being allowed to affect the story, it makes sense you have to pay to have that label narrated in a scene and thus allowed to affect the story.
If you want to houserule in actual character-trait level things into 3.0, as my 3.0 GM does, what you can do is charge a refresh to upgrade an aspect to a FATE 2.0 aspect, with all of it's normal rules and implications in addition to the 3.0 rules. (Obviously, you refresh you aspects in 3.0 when you... refresh. As in when you get the fate points for your leftover refresh points) This is a generally underpowered option, but helps players who like stories that have consistent characters in them get along somewhat better in the no-longer-playstyle-agnostic editions of Fate.