I didn't say she was weak early. I said she only has one stun, which is single target. She can engage but only disable one of you. I've found the best way to deal with Leona engaging is to fall on her ADC. Whether you're the ADC or Supp forcing them to deal with the target that Leona didn't hit reduces her effectiveness a lot, or highly damages her ADC whom she can't sustain well (with only so many triggers from Relic, a lot of which are used immediately with no heal benefit).
You're Soraka? She jumps on your ADC, drop your Q and E on her ADC and heal yours after you get Rejuvenated. You'll win that exchange most of the time and your ADC can start following up if their ADC stays around to get rooted. Zyra? Give her ADC a bunch of plants to deal with, they either back off or take a lot of damage from you. Any ADC? If their ADC goes for your support and not you deal a lot of damage to them. Supports start with three pots, so ADC health is more "valuable" early game because they only have one. You win that trade by doing that. Unless you're low enough for them to kill you, but since Leona's poke is nonexistent you should be practically full health at level 3, so shame on you if you are.