In my experience, much like Grits, being alone only fueled my alcoholism. I became a full-time isolated user for about 1.5 years and I lost my job and nearly killed myself and have the ER visit bills to prove it.
Once you're comfortable in basic sobriety, (as was stated above) it's all about changing people, places, and things. Ditching your old buddies is probably for the best - but how are you going to fill that hole? What are you going to do with your time? When you say "focus on sobriety and losing weight", I'm guessing you don't just sit down at the kitchen table and stare at books whilst munching on lettuce for 8 hours. You're probably sitting around, surfing online, on the same damn sofa you sat on when you were 12 years old. And that's not going to help anything.
Losing old relationships is fine, but find a new hobby or interest to replace them. Being alone is fine too - as long as you aren't replicating the same behaviors you were when you were an active alcohol user. And maybe it might be time to move out of your mum's place sometime - how about making that a goal?