"and I don't mind a little extra weight"
Famous last words
Keep in mind that this is a LIGHT weight forum (light being not heavy as opposed to not dark ), so answers are going to reflect that. You need to answer a few questions first.
WHY do you NEED a lantern?
Do you want to throw a lot of light everywhere?
What tasks do you need all that light for?
Why isn't a head lamp or flashlight enough?

Personally, I don't need a lantern. And if I was to bring one, it would be a candle lantern. My head lamp is VERY adequate for anything I want to do. Combine that with a small flashlight and/or campfire, and all my lighting needs are met. I don't need to sit around after dark in the light. Especially something that attracts insects. I go backpacking to come closer to nature, and a lantern would only place me farther away. I love it when my eyes adjust for the darkness, and I can see without a light. I have done many hikes in total darkness, and loved it. I probably should restate "total darkness" as moonlight. Full moons are amazingly bright. Full moons on snow are even brighter. When I was a boy scout, we would always play "Capture the Flag" for hours in the dark, no flashlights. I would say that on average, I use my flashlight/headlight for about 20 minutes each day on a trip. But, this is just me. Maybe you are different. I will let you carry a heavy lantern. Now, as for batteries vs fuel, I would think that a lantern with batteries is lighter than a lantern with fuel and fuel bottle. Especially since the lanterns that use fuel have to be heavier just to be able to use the fuel. But, I haven't done the calcs so I could be wrong.