Sometimes, when starts at a lower dose, it is to check that certain harsher side effects are not present before going up to the therapeutic dose.

It is less likely (but not impossible) that some side effects may appear at a higher dose. (not talking about toxicity at extremely high doses)
IF you had side effects at a lower dose, which disappeared, then that has more of a chance of producing the same side effect again at a higher dose.

Some medications, such as Seroquel, work on the paradoxical action where a certain side effect is more present at a lower dose.
In the case of Seroquel, the lowest dose used (25 mg) typically causes drowsiness and is therefore used for a long term sleep aid. Higher doses do not have this sedating effect because at a lower dose, the majority of it binds to the histamine (H1) receptor and cause sedation.

Similarly, this is why some side effects are more present in certain medications- because the medication may also bind to another receptor (not the target receptor) and cause a certain effect.