Is this design in 3NF? Why to choose another design not in 3NF
Both designs are technically 3NF, depending on your data population.

What a lot of people who have only a cursory understanding of formal normalization theory don't understand is that redundancy in foreign keys isn't really redundancy by definition.  Transitive dependencies and partial dependencies apply to the way non-key attributes relate to key attributes.

If your composite keys happen to contain (or even consist of) foreign keys then whether your foreign key has the look of being denormalized isn't relevant.  (i.e. Design 1 isn't redundant in a way which is significant to the formal definition of normal forms.)

The practical issue comes down to what the values of your keys are.  If you have natural keys and the Part key consists of IDObject=123 and IDPart=1 - i.e. your IDPart values are natural number sequences which are only unique within the context of a given IDObject value, then you need to use design 1 (weak entities).

However, what a lot of people do for good (and less good) reasons is apply surrogate primary keys to every or nearly every table.  I'm not going to get into whether or why to use surrogate keys.  That is a holy war for another question.  However, if you happen to have table-wide unique (e.g. IDENTITY) values for IDPart, then your primary key for Part is more complex than it needs to be using design 1.  In that case, there is no need for IDObject in the PK of Part because the table already has a unique key just using IDPart.  In such a case, design 2 is sufficient and simpler, therefore better, as a rule of thumb.

In practice, I would say weak entities are much more common in logical models than in physical models, if for no other reason than that most physical models tend to use surrogate primary keys.