Hi,
Welcome to the Forum.
Yes, that is the mark of the Weidlich Sterling Spoon Co., see:
http://www.925-1000.com/ax_weidlich.html
As for the other mark, that could be anything, an internal factory mark, a weight indicator, a jeweller or personal inventory mark, etc.
In 1952 the patterns and dies of this company were acquired by the Web Jewelry Mfg.Co.. I do not know if they also acquired the use of the name, but if so, could that be an upside down 'W'? Just an absolute shot in the dark.
Trev.