Partial cover and concealment are identical to cover and concealment.
It's a confusing terminology change that happened part-way through 4e's lifespan, not the addition of an extra level of cover and concealment. The modifier "partial" was added to 'normal' concealment --probably in a well-meaning effort to clarify things-- and both the Rules Compendium and the Online Compendium parenthetically note that it is "sometimes simply called 'concealment.'" (RC 222)
The Online Compendium's glossary entry on cover still hasn't appended the modifier "partial," nor does it note that this word might sometimes be added, but the Rules Compendium uses the phrase "partial cover" and adds that it is "sometimes simply called 'cover.'" (RC 220)
Keep an eye on "superior" and "total," too.
There is equal potential for confusion in the upper echelons of cover and concealment: better cover is called "superior cover," while excellent concealment is "total concealment." I see no particular reason these two similar effects should have different modifying terms, and am surprised that only one item (the Nightmare's Keen Senses from DR 393) is currently confused by this (according to a search of the Online Compendium at the time of this post).
The answer to your question is - there is more than one kind of illusion.
Glamers and figments change your senses, so they can't hold up weight. Characters trying to stand on them will fall through (and immediately disbelieve, since they have proof the illusion was a fake).
A figment spell creates a false sensation...
A glamer spell changes a subject’s sensory qualities...
Because figments and glamers are unreal, they cannot produce real effects the way that other types of illusions can.
Shadows can hold up weight just fine.
A shadow spell creates something that is partially real from extradimensional energy. Such illusions can have real effects.
However, some shadow spells can be partially disbelieved, in which case there is a % chance that the object doesn't "work" and the creature falls through. See shadow conjuration:
Shadow objects or substances have normal effects except against those who disbelieve them. Against disbelievers, they are 20% likely to work.
Patterns and phantasms affect the mind directly. These illusions can make someone believe they are standing on the floor, while in reality they have fallen down a pit.
Like a figment, a pattern spell creates an image that others can see, but a pattern also affects the minds of those who see it or are caught in it.
A phantasm spell creates a mental image that usually only the caster and the subject (or subjects) of the spell can perceive. This impression is totally in the minds of the subjects.
For any non-instantaneous spell, the effect disappears once the duration ends. Regardless of what kind of spell was creating the bridge (illusion, conjuration, evocation, what have you) the creature standing on it will fall in the hole.
Best Answer
No, but it can provide obscurement.
Cover requires a solid object. Examples from the definition:
The game mechanic that represents the sight-blocking effect of something like an illusion is obscurement.
Note that the main effect of the blinded condition is disadvantage on attack rolls, not a change in the target's AC.
What if the attacker knows it's an illusion?
Minor illusion, silent image, and major image all specify that a creature that discerns that it's an illusion can see through it. If it's an illusion of, say, a wooden fence, this will happen the first time an attack hits the illusion. On the other hand, if it's an illusion of something like dense fog, an arrow or other object passing through it is perfectly normal. A creature can always spend a turn examining the illusion to make an Investigation check to see that it's not natural, but it's basically impossible not to metagame that.
Even after the enemy discerns the illusion, it is still there being a distraction. I'd downgrade it to "lightly obscured", which just imposes disadvantage on Perception checks in the area, but that's a judgment call.