Hi Bill. I did not find any Joshua Weld in our index. There were however, 13 men named Weld, all of whom were from MA. Those men and their birth years are:
Aaron 1726
Caleb 1759
Calvin 1761
Ebenezer 1747
Eleazer 1737
Habijah 1702
Isaac 1754
Jacob 1752
John 1752
John 1730
Joseph 1728
Moses 1757
Walter 1761
It could be that if Joshua did not serve, perhaps his son - and your ancestor - did, which is why I listed the men and birth years. If any of these are your ancestor, let me know and I can send you back what was found on any of them.
Not finding your Joshua only means that no woman since 1890 has entered DAR using him as her patriot ancestor. It appears you know a great deal on Joshua already. Perhaps you have enough to enter SAR yourself. Should you have female children, cousins or siblings, who are of the same line, they could enter DAR using Joshua. If you would like a contact made from a member of the Sons or Daughters of the American Revolution, let me know the city and state of your residence and we'll see that is accomplished. There are men and women in each organization whose job is to help prospective members like yourself.
good luck!
Mary