I'm leaving my data here since I tinkered around with... extra methods.
Test 1: Raphael - 74 strength, B support, E Heavy Armor: No luck
Test 2a: Leonie - 74 strength, C support, D lance: No Luck
Test 2b: Leonie - 21 Strength, C Support, D+ Lance: Recruited
Test 3a: Dorothy - 20 Charisma, No support, C+ Authority: No luck
Test 3b: Dorothy - 20 Charisma, C Support, C+ Authority: Recruited
Test 3b: Dorothy - 21 Charisma, No support, C+ Authority: No luck
I tried to raise my Cha higher, but after 8 tea times of not getting more Cha, I give up. Cha is hell.
Theory based on findings - I think there's a baseline on the weapon skill that you need to hit for them to be interested. The stat requirement is reduced by supports. Of course this could vary by characters them self too. Who knows.
(Edit)
Test 4a: Hilda: 21 Cha, D Axe, C Support = rather interested.
Test 4b: Hilda: 21 Cha, D+ Axe, C Support = rather interested.
Test 4c: Hilda: 21 Cha, D+ Axe, B Support = Join
Test 4d: Hilda: 21 Cha, D Axe, B Support = Join
Test 4e: Hilda: 20 Cha, D+ Axe, B support = rather interested