Really? Aztec skirms are a great counter against HCs (+1 range is helpful for that), and monks counter BBC (and Aztec monks are the best in the game). Looking at their best 5 and worst 5 matchups in all games and 1200+, I see they do well against Bengalis, Bohemians, Italians, Koreans, and Vietnamese. They do poorly against Malians, Romans, Georgians, Mongols, Sicilians, Japanese, Vikings, and Spanish. SMUM’s pics of top/bottom 5 civ matchup’s also included Britons and Dravidians as Aztec’s best matchups, and Franks as a worst matchup
Of the civs they do well against, Bohemians, Dravidians, Gurjaras, Italians, and Koreans have both HC and BBC (some with bonuses to them that drastically improve hand cannon and BBC play - sometimes to the point of making it a go-to strategy, especially for Bohemians). The civs that lack one or both are Britons, Vietnamese, and Bengalis.
Of the civs they do poorly against:
- Romans, Mongols, Sicilians, and Vikings have neither
- Georgians and Japanese miss BBC
- Malians, Spanish, and Franks have both
These results all have a high degree of uncertainty, so I can’t say that any of these civs are certainly in the top 5 or bottom 5, but they do strongly suggest a good or poor matchup. Based on the number of gunpowder civs that they do well against (notably including Bohemians), I think I can safely say that the stats don’t show a weakness against HC/BBC. If Aztecs had a weakness against those, I’d especially expect Bohemians to do well against Aztecs (given that they often go for hand cannons in castle age and that they have Houfnice). But there also civs that have both in Aztecs worst matchups. It should be noted that HC/BBC can only matter if a game gets to imperial (excluding Bohemians), and Aztecs can try to kill an opponent well before then.
TLDR: stats don’t show that, and Aztecs have a counter to both among their stronger units (namely monks and skirms)
Teutons get +1/2 MA (for infantry and cavalry). It’s nice, but doesn’t address infantry’s weaknesses - cavalry remains the go-to for Teutons.