A shield isn’t a weapon. Otherwise the Duelist style wouldn’t work with a shield, which Sage Advice says it can.
@mackenzie884 A shield certainly isn’t a weapon, but like many things, it can be used as an improvised weapon.
— Jeremy Crawford (@JeremyECrawford) November 17, 2015
An improvised weapon is a weapon. It’s right there in the name: Improvised WEAPON. If a shield is an IW then no Duelist
@mackenzie884 An improvised weapon is, indeed, a weapon, but only the moment it’s used as such. A chair/shield/etc isn’t a weapon otherwise.
— Jeremy Crawford (@JeremyECrawford) November 17, 2015
So now I can have Duelist +2 dmg, Shield +2 AC, AND a second IW attack? Yes/no?
@mackenzie884 In this scenario, how are you getting a second attack with the shield?
— Jeremy Crawford (@JeremyECrawford) November 17, 2015
The shield is an IW off-hand. Attack #1 longsword, bonus action attack #2 with shield. In attack #1, Duelist is satisfied?
During my Longsword attack, is the Duelist condition satisfied? Then I make an off-hand IW attack on my bonus with shield.
@mackenzie884 I’ll ask my question differently: what game feature is letting you attack with the shield as a bonus action?
— Jeremy Crawford (@JeremyECrawford) November 17, 2015