Are you updating an existing field? Or creating a new one and adding a value?
The CustomMetadata and the CustomObject are two different Metadata types, but under CustomMetadata you will find the "values of the fields created in the CustomMetadata" and under CustomObject you will find the CustomMetadata object itself.
For instance, a CustomMetadata named "Off Limit Settings" with a number field named "AccountOffLimitMonths" will be shown as a CustomObject like (file: objects/Off_Limit_Settings__mdt.object):
<?xml version="1.0" encoding="UTF-8"?>
<CustomObject xmlns="http://soap.sforce.com/2006/04/metadata">
<fields>
<fullName>AccountOffLimitMonths__c</fullName>
<externalId>false</externalId>
<fieldManageability>DeveloperControlled</fieldManageability>
<inlineHelpText>Lorem ipsum dolor</inlineHelpText>
<label>Account Off Limit Months</label>
<precision>18</precision>
<required>false</required>
<scale>0</scale>
<type>Number</type>
<unique>false</unique>
</fields>
<label>Off Limit Settings</label>
<pluralLabel>Off Limit Settings</pluralLabel>
<visibility>Public</visibility>
</CustomObject>
And the field will be shown under CustomMetadata as (file: customMetadata/Off_Limit_Settings.Off_Limit.md):
<?xml version="1.0" encoding="UTF-8"?>
<CustomMetadata xmlns="http://soap.sforce.com/2006/04/metadata" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
<label>Off Limit</label>
<protected>false</protected>
<values>
<field>AccountOffLimitMonths__c</field>
<value xsi:type="xsd:double">12.0</value>
</values>
</CustomMetadata>
If you want to add a new field, modify the first file and deploy it in a package. If you want to modify a field, use the second file.