Is it better to lift lift 2 weights (free) at the same time or to alternate arms with the weights?

It depends on what I'm trying to do.

For general strength I'll use a bar or dumbbells. I feel like the bar lets me use a little more weight, since there isn't side to side play, and the dumbbells allow for a change in form, such as a biceps curl to the inside vs outside.

When I do one at a time is when I really want to focus and isolate the one arm. Less weight, but more control over form and things like the angles to hit diff muscles.

Sometimes two helps you balance out also. Depends on the exercises.

How about just regular biceps curls?

Same thing there.

I'll use a bar or two dumbbells when I'm doing general lifting... as you are working both arms at once, decreases time it takes to work both arms.

But you can also really work the diff areas of the muscle doing one at a time.

Try this: put a dumbbell in your hand. Take the other arm and put it across your ribs, horizontal, and resting against you. Place your other elbow with the dumbbell on top of that arm, usually on the top of your hand.

So you've got the one arm supporting the elbow of the hand with the weight. Then do carefully controlled biceps curls, keeping the hand with the weight coming straight back toward your shoulder. Do this a bunch of times.

Then change the curls by pushing the weight more toward the outside. You'll feel this work a diff area some. Then do curls angling toward the inside.

By changing the angle, and slowly moving through the motion, you can hit diff muscles.

But again, it depends on what you're doing. Stamina comes from lighter weights, more reps. Muscle mass comes from more weight.

Even with a bar you can move your grip wider or narrower to stim the biceps differently.

The big thing you should focus on first is good form. Either use a trainer, work with someone who knows, or even pick up a book.

HI,
The answers before mine are very good.
When I use to workout, many years ago, I went for "muscle".
By that I mean, building up muscle.
I used a bar, with as much weight as I could lift, doing different excercises.
Then, used a set of barbells, doing individual excercises with each arm separately. It worked very well.