On the topic, this is a nice article with historical weight data for Mustangs from CJP.
https://www.cjponyparts.com/resources/mustang-curb-weights
Out of curiosity I wanted to see for the first generation, what was the bigger engine available and the maximum weight listed for the fastbacks (which is likely the one with the biggest engine). Data from CJP article and Wikipedia. Please make corrections if needed. The data for 1967 is conflicting.
1965: 2,914 lbs, 289 Windsor
1966: 2,978 lbs, 289 Windsor
1967: 2,919 lbs, 390 FE (Weight here does not make sense so this data may not be accurate)
1968: 3,362 lbs, 428 Cobra Jet
1969: 3,463 lbs, 429 Boss
1970: 3,472 lbs, 429 Boss
1971: 3,607 lbs, 429 Cobra Jet
1972: 3,437 lbs, 351 Cleveland
1973: 3,521 lbs, 351 Cleveland
The point is that the cars became generally heavier due to the bigger engines, which meant beefier bodies and drivetrain. Also bigger noses to fit the bigger engines.