The "heavy bastard sword" is not the same as other weapons with the label "heavy", it's just another type of sword, not a bastard sword with a modifier. Because of that you'll notice "Tempered/balanced Heavy Bastard Swords" appearing in stores.
As to the modifiers certain ones only appear on certain weapons.
Axes, polearms, crossbows (except for the Heavy crossbow) and hammers get the "Heavy" modifier instead of Tempered. Heavy increases damage whilst lowering speed. Some swords may also have "Heavy" versions.
Swords get "Tempered", which slightly increases speed and increases damage.
All melee weapons get a "Balanced" modifier which increases weapon speed and damage to a small degree.
Bows get "Strong" (except for the Strong Bow, which only has a Masterwork version), which increases damage, and lowers speed by a small amount.
"Masterwork" bows increase damage to a greater extent than the "Strong" version, but increase the power draw requirement significantly. The same applies for "Masterwork" crossbows, but with strength requirement increased instead.
"Thick", "Reinforced" and "Lordly" armour increase the armor value of the weapon, with each greater than the last.
"Heavy" Horses have greater charge, armor and health values, "Spirited" are faster and more maneuverable and "Champion" are better than both. Whilst "Lame" refers to a horse that has been injured, but leaving them in your inventory for a week without riding them will cause them to recover to the stats of a normal unmodified horse.
And all the negative modifiers, like "Rusty", "Chipped" and "Swaybacked" are all pretty self explanatory.
Hope that helps.