Lyric discussion by 40zebras 

I hear the lyrics a bit differently.

I fell asleep in the silence before the stream fights the fire free in the world that you've given lay in the sand the water still calls still calms

(My take in this verse is that someone has left her. She's free because this person has given her a world without him or her in it. She's alone - fell asleep before the tides came in to douse the campfire - OR if metaphorical - before the tears washed away her passion or anger. She's resting on the beach because the sound of the waves sooth her.)

Afraid of the dark that surrounds you hiding the dirt from the ground breathe the wind that surrounds me I'm not afraid to sleep in the night not afraid to sleep in the night

(Either she is free of guilt that would otherwise keep someone awake OR after taking a deep breath of fresh air, she's no longer afraid of being alone.)

Free like a bird with no holders holding the weight of the sun I know the road that you send me I know the way it leads to one

(No one holds the bird in captivity, but it is not free. It is encumbered by the weight of the sun - the light, the truth. The truth is his or her road does not include Hope or only provides one option as Havenspear noted.)

Real like the bones in my body real like the flesh that covers the grape it's real like the flesh that covers the grape

(She knows it to be true. By the way: "real like the flesh that covers the grave" only makes sense if the bodies are fresh and technically, it wouldn't COVER the grave.)

Wait for the guards that you send me before i will show you myself wait for the storm that comes to me maybe i'll just change my mind

(So she won't speak to him or her until she hears from one of his friends - perhaps overprotective friends. Or until she's so angry, she has no choice but to confront him/her - but then again, maybe she'll just say, 'forget it.')

Plea for the will of forgiveness I'm not afraid to say I was wrong I was wrong maybe I was so wrong so wrong

(Still, either shes wishes to forgive him/her or is pleading for her/him to forgive her. She may have been the problem. It seems as if she is directing the "I'm not afraid to say I was wrong" line to the person in question, then it shifts inward so she is speaking to herself: "Maybe I was so wrong." There's doubt there.)

As for the title, she is as physically free as a bird, but emotionally she is not. She's carrying the weight of the sun - the recognition of her role in whatever falling out she sings about.

My Interpretation
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