From the patch notes:
"Blood Weapon now applies an effect that reduces the TP cost of weapon skills by 20%."
Assuming 0 skill speed (it won't be, but lets assume), without BW:
15s = 6 abilities = 2 combos of 190 TP each = 380 spent. Recovery is 60TP every 3s, so 300 recovered for net -80TP
With BW:
15s = 7 abilities = 2 combos of 190TP plus an addition 70TP = 450 spent, less 20% = 360 spent. Net -60TP
It seems to me as if the offset really doesn't help TP issues that much, but it's nice to know at least now using BW won't make you run dry even more quickly.