Hi Gill
The idea of these medicals is to find out whether you're likely to be a 'burden' on the NZ health system. Being overweight may not mean that you'll be banned from proceeding with your application, but it could well mean that you need to undergo further tests for things like diabetes or other conditions that can result from being a bit on the cuddly side.
If you are failed on these grounds, there is such a thing as a medical waiver that you may be able to apply for. It can allow those who have certain medical problems yet could still be of considerable use to NZ to get in.
From the INZ Operations Manual....
A4.60 Applicants who will not be granted a waiver (26/07/1999)
See A4 Effective 28/11/2005
See A4.60 Effective 13/12/2001
Applicants will not be granted a medical waiver if:
they require dialysis treatment, or a consultant physician has indicated that they will require such treatment in the immediate future; or
they have active tuberculosis (see A4.60.1 below); or
they have a mental disorder or intellectual handicap that has needed care in a hospital or supervised residence for more than 90 days in the last 2 years; or
they have a physical incapacity that requires full-time care.
Then.....
A4.70 Applicants who may be considered for a waiver (26/07/1999)
See A4 Effective 28/11/2005
See A4.70 Effective 01/04/2004
Applicants other than those in A4.60 and A4.60.1 may be considered for a medical waiver. Visa and immigration officers must consider the circumstances surrounding the application to decide whether they are compelling enough to justify making an exception to the acceptable standard of health requirement (see H2).
Factors that officers may take into account in making their decision include but are not limited to the following:
the objectives of the relevant residence policy or category, and whether New Zealand has sufficient resources, and
the degree to which the applicant would be a burden on New Zealand health services, and
whether the applicant has a spouse or partner who is a New Zealand citizen or resident 
, and
whether the applicant has immediate family lawfully and permanently* (see F4.1.1) resident in New Zealand, and
whether the applicant's potential contribution to New Zealand will be unique, and
the applicant meets all other requirements of the Humanitarian category (see H2).
Then.......
A4.60 Medical waivers (applicants for residence)
See A4 (before 28/11/2005)
Applicants for residence in New Zealand who are assessed as not having an acceptable standard of health and whose applications meet all other requirements for approval under the relevant Government residence policy may be considered for the grant of a medical waiver unless:
they require dialysis treatment, or an Immigration New Zealand medical assessor has indicated that they will require such treatment within a period of four years from the date of the medical assessment; or
they have active pulmonary tuberculosis; or
they have severe haemophilia; or
they have a physical incapacity that requires full time care.
Medical waivers will also not be granted to people:
who are applying for residence under Family category policy; and
who were eligible to be included in an earlier application for residence as the spouse or partner of a principal applicant or the dependent child of a principal applicant or their spouse or partner; and
were not declared on that earlier application.
People who:
were eligible to be included in an earlier successful application for residence as the spouse or partner of a principal applicant or the dependent child of a principal applicant or their spouse or partner; and
who were declared in that application but were not included in that application as non-principal applicants; and
whose application for residence under Family category policy is sponsored by a person included in the application for residence referred to in (i) above
will be assessed for the grant of a medical waiver as if they had been included in the earlier application and as if the sponsor was not resident in New Zealand.
Applicants (and dependants included in their application) who have been recognised as refugees may be granted medical waivers.
There's also another
old thread where we discuss more about medical conditions and waivers that might give you more information.