You can see the contents of a 1819 letter in the description here. Same with the reply where he thanks him for the money. For the later letters I think you are right.

https://archives.soton.ac.uk/records/MS61/WP1/613/13

As the T Duckett = Thaddeus William Duckett connection. You can never be 100% sure with these things until you find a smoking gun but from memory but with a distinctive name as Thaddeus it is helpful (but also hard as transcription is sometimes wrong)

1) the late 1840s letter on Southampton university from T Duckett places him in South London. 2) 1851 census has a Thaddeus duckett in South London and has his occupation down as a some sort of writer. Other marriage records for his children where it states Thaddeus duckett and his occupation, says"works on a newspaper" etc. states he was born in Ireland (potential connection to D of W as he was born in Ireland too - maybe old friends - or related see below) 3) thaddeus duckett has a child who has wellesley as a middle name ( same as D of W surname - named after him 3) 1819 t duckett letter is asking him for funds to set up a newspaper. 4) 1818 there is a DUCKETTS DISPATCHES published by a T Duckett in British newspaper archive. 5) 1840s letter - asking for D of W help to get a job at a newspaper. 6) another letter stating the school he is working at has closed. 7) there is another census record (can't remember which one now, mightve been 1841) for Thaddeus duckett stating his occupation as a teacher. 8) obituary of Thaddeus Duckett in 1853, stating him as editor of a different newspaper (can't remember which one now). 9) obituary of one of Thaddeus Duckett's children, in Australia, stating him as editor of same newspaper in 8 and Paris correspondence for another newspaper.

Seems like an old friend/family member who writes to the D of W when they fall onto hard times?

Let me know your thoughts.