Hello
St Johns Terrace is there on the 1891 census with 17 houses
no 17 a Marrianne Beck 44 was running a ladies school
no 16 has the girls
no 15 army Captain Robert C Coote 65 widow and family
14 unoccupied
13 more of the school with staff and girls.
12 Augusta Thompson widow 60 from Bombay
11 Ingram Chapman Major General 66 and family
n0 10 empty
no 09 a lodging house run by Matilda and Eleanor Tucker 56 and 46
no 8 empty
no 7 lodging house Williamd and Elizabeth King 75/60
no6 Henrietta Hodding 48 and her school
The rest are private house for the rich all living on their own means with servants and family
William and Matilda Coker 87/71,no4 Lillias Williams 49,Lillian47,Alexander 33 widower,no3 Ellen Thompson 60,no2 Mary A East 93 widow and children and no1 Pauline Gattwood 39 widow.
1881 no2 is still Mary East
n04 lodging house
n06 Proff of languages with students
no7 lodging house
n0 9 still the Tuckers
n0 10 school Gertrude and Cellia Parker 45 and 44
13-15 empty
no 16 is now the Vicarage for St Johns Weymouth.
1901 as you say it's not there because it's Dorchester Road (no 21 is a lodging house run by Lucy Galpin 71 but it may not be the same house))and it doesn't seem to be on the 1871.
This website may help
www.weymouth-dorset.co.uk/streetweymr.htmlUnfortunately I can't have a look myself as my local council have blocked it supposedly because of unsavory material.
It does seem to have a connection with St Johns parish church
Ciderdrinker