If he's throwing tantrums which result in you picking him up then I suggest you stop responding to the tantrums. It's teaching him that all he has to do to make you pick him up is throw a tantrum, so it just makes it worse iykwim.
Can you point out other kids and compliment them on how they walk by themselves? I find that positive reinforcement (even if it's directed toward someone else) has big results. I do this in my classroom all the time, like if I see a student slumped over I won't say anything to him but I'll look at the little girl next to him and say "I like how Sofia is sitting up straight and tall!" and then suddenly the whole class sits up.
You can also reward him for walking on his own. If you know you're leaving the house and you suspect he'll throw a little tantrum once you're out there get him prepared and tell him that if he can walk by himself all the way to wherever you're going he's going to get a treat out of it like extra time at the park or something.