Oh to those of little faith...
I have been refurbishing Triumphs for several years and what I have found is
some of this stuff is not rocket scientist stuff.. does not take a four year
degree or specialized training or equipment.  That is not to say you should
not employ common sense and good judgment.  I certainly trust my seatbelts
that have had new webbing sewn in, over old belts that have been compromised
by age, heat, UV light, wear & tear from kids, dogs, and what not.  Follow
the pattern of the original stitching, maybe add in some extra, and you
should be just fine.  Don't use any household thread, get commercial
upholstery thread (about $4 for a large spool), or for the real serious, use
Kevlar thread from a sail shop.  At least if they fail you have no one to
blame but yourself.  Please don't sue me as I cannot guarantee your handiwork.

Cheers,
Kevin