Loyalty
Loyalty is based on several factors, the most common are Bailiffs and Fief Expenditures. Good Bailiffs are simply a matter of their stats . However, expenditures are another story. One must juggle the loyalty gain against the surplus gain. Loyalty will increase most dramatically if all expenses are maxed out. Thus if you have a fief that has a low loyalty (3-5) then one should consider maxing out all expenses to give the maximum increase of loyalty. Once the loyalty is up then one can adjust the expenses as needed for the financial side.
Another time one needs to adjust loyalty is when tax rates are low. Note a low tax rate causes industry to grow more. Though if you have no industry, the growth is virtually no nonexistent. One should want to increase the tax rate to bring in more money. However to jump from 5% to 20% would result in a dramatic drop in loyalty and possible rebellion . So gradual steps are needed. Along with max spending, the small increase in taxes (and decrease in loyalty) will be offset by the max spending increase of loyalty.
Best advise - slowly increase your taxes - at low levels of taxes (1-5) small increases of .5 to 1 percent is best. When in the 15 to 20 range a larger increase can be done. I have done 5% in this area and been okay though the loyalty does take a hit.
It's a good idea to wait until you have about 6 loyalty before increasing the taxes. And if it goes below 5, allow the loyalty to increase.
Another way one can increase taxes is wait for the loyalty to reach 9 and then increase the taxes - but this tends to take more time. One reason is (and this is especially true for French fiefs,) the population is so high that most can only maintain the average expense and loyalty is slow in coming. Thus if you wait for the loyalty to raise with fief expense at 5% one will wait a long time. Whereas, the higher you get your taxes the more you can spend and more increase in loyalty you can get per season.