I'm assuming you are wanting to replace JakMasterId with an auto-increment field so the other two tables don't need a varchar(60) field and to improve query times, but that you are keeping JakMasterId as information.
-- set database single-user
-- drop foreign keys
create table NewMaster (ID int identity(1, 1), JakMasterId, Date))
insert NewMaster(JakMasterId, Date) select JakMasterId, Date from JakMaster
drop table JakMaster
sp_rename 'NewMaster', 'JakMaster'
alter table JakToRoad add MasterId int
alter table JakToBig add MasterId int
update JakToRoad set MasterId = JakMaster.ID
from JakToRoad
inner join JakMaster on JakMaster.JakMasterId = JakToRoad.JakMasterId
update JakToBig set MasterId = JakMaster.ID
from JakToBig
inner join JakMaster on JakMaster.JakMasterId = JakToBig .JakMasterId
alter table JakToRoad drop column JakMasterId
alter table JakToBig drop column JakMasterId
alter table JakToRoad add constraint FK_JTRtoJM foreign key (MasterId) references JakMaster (ID)
alter table JakToBig add constraint FK_JTBtoJM foreign key (MasterId) references JakMaster (ID)
-- reset database to multi-user