"very" and "too" are both terms that add weight to the thing they are modifying, but "too" also connotes that the added weight is to excess. "only too" is an idiom, the meaning of which depends on the context.
In positive declarations, the "only too" idiom is closer to the meaning of "very" than to "too". It does not connote an actual excess of something, but rather employs exaggeration as a device to give emphasis. For example, "I would be only too willing to help" expresses that the speaker would be very willing to help, their willingness emphasized by the suggestion that their willingness might even border on the extreme.
In negative declarations, the "only too" idiom may also mean "very", but can mean "too" as well, adding a sense of wrongness. For example, "his death came only too soon" expresses not only that the death came too early, but that it shouldn't have happened so early.
See "only too" in macmillandictionary.com