Yes, Weaken can be Insidious
The Insidious modifier can be added to any power, though the Descriptors may require some thought and revision to make sense.
But How Does It Work?
Keeping in mind the Insidious description:
This modifier is similar to the Subtle modifier (later in this section), except Insidious makes the result of an effect harder to detect rather than the effect itself. For example, a target suffering from Insidious Damage isn’t even aware he’s been damaged. Someone affected by an Insidious Weaken feels fine until some deficiency makes it obvious that he’s weaker, and so forth. A target of an Insidious effect may remain unaware of the danger until it’s too late!
An Insidious effect is detectable either by a DC 20 skill check (usually Perception, although skills like Expertise, Insight, or Treatment may apply in other cases) or a particular unusual sense, such as an Insidious magical effect noticeable by Detect Magic or Magical Awareness.
Note that Insidious does not make the effect itself harder to notice; apply the Subtle modifier for that. So it is possible for an active Insidious effect to be noticeable: the target can perceive the use of the effect, but not its results: the effect appears “harmless” or doesn’t seem to “do anything” since the target cannot detect the results.
How would Insidious work on Weaken Senses?
Like any Insidious effect, the results are not apparent until the failure becomes obvious. For a Sense power, that's when it becomes obvious that the character failed to detect something they normally detect.
The Senses power is an extension of normal sensory input. That's what the related "Under the Hood" sidebar is about.
People and characters ignore much of their sensory information all the time, focusing on current tasks or sensory changes. An easy example: remember what your mouth tastes like, or what your skin smells like.
Without a prompt, information like that doesn't come to conscious (i.e. obvious) attention unless it changes. If you cut your cheek and start tasting blood or get dirty and notice the new smell of your skin then you pay attention, otherwise you ignore that data. The same is going to be true for a character with the Radio sense or Accurate vision or Darkvision - unless the situation is actively drawing attention to that sensory power, the character is almost certainly focusing on other inputs and issues for at least some time. And when they start using it, it seems to be working fine - this person must simply be concealed from it! Because invisible foes are much more likely than your own powers failing; the latter has yet to happen but the former has happened five times that you know of.
There are a few Descriptors where that doesn't work. (A malfunctioning technological display, that automatically gives the precise range to anything aligned with the targeting reticle, will be easily noticed by the operator.) Which is why GM adjudication is so important, and foundational, in the Mutants & Masterminds rules.