I'm a plus size mama too, so I've had to try out a lot of different slings and packs to see what worked for us. We have waaaay too many baby carriers, but these are the ones we use the most:
OTSBH padded sling in XL: I use this when popping in and out of the car for errands. Goes on quickly, she's snuggled up to me so strangers don't poke at her, and the padding is comfortable on my shoulder. I don't use this sling for long wear because my back muscles start to hurt.
Baby Bjorn with extra long straps: both DH and I use this for long walks and grocery store trips. Leaves my hands free, DD loves facing out, and I put a couple of those padded car seatbelt covers where the straps are over my shoulder and it's heavenly. Also stresses my back when I wear it too long, but that's usually after like an hour long walk.
Hip Hammock: DH uses this more often than I do. I was worried when I ordered it that the waist strap wouldn't fit me, but it does. I find this less comfy than the OTSBH but DH loves it for ease of use and how comfortable she sits on his hip. Not exactly hands free, requires you to reach one arm around the baby to do things in front of you, but it works really well for them.
I used a New Native style XL sling for DD when she was tiny, but we are both less comfortable with it now that she is bigger. She's 6 months, 28" and about 16 lbs.
Well, this post was all about me, but I hope you find it helpful.