Sif allowed Thor to enter Frigga's room first especially as he was the King of Asgard and Frigga's son. He should have first honour of clasping eyes on the previously deceased Queen mother. And she was if nothing else alert and wary, ready to have Thor's back at any given second should this prove to be some sort of twisted lie.
Hopefully it would not but Sif did not wish to raise her hopes in case they were crushed.
She watched as Frigga and Thor embraced, dark eyes ticking over every small detail of Frigga's face as if it were the first time she had seen it. She looked, talked, and moved like the Frigga she loved and lost but she was still... reserved.