How to secure a top heavy tall iron headboard
That frame is built of heavy-gauge steel and will likely hold up your headboard without damage. The fact that your headboard is vertical means that there's relatively little stress on the assembly. 

However, there may be play in the rivets and other connections which leave the headboard a bit wobbly when the bed is used. To completely remedy that you'd probably need to add a diagonal brace near the floor, between the horizontal frame rail and the headboard leg, creating a larger gusset. You could do so with a simple double-bent 1/8" steel or 1/4" aluminum bar stock attached with carriage bolts. Something like so:

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