When I try your code as-is and execute the proc I am not seeing any locks opened against TableB which is what I would expect since no FK columns are being affected. Did you maybe pare down the proc too much? Does the actual proc also contain ObjectID in the SET-column-list?

After changing your sample proc in this way I was able to start seeing locks opened on TableB due to the FK with ON DELETE CASCADE.

ALTER PROCEDURE [dbo].[spUpdateObjectHeader]

@objectID INT,

@ColG VARCHAR(64),

@ColH VARCHAR(64),

@ColI VARCHAR(64),

@ColD DATETIME

AS

UPDATE TableA

SET [ColG] = @ColG,

[ColH] = @ColH,

[ColI] = @ColI,

[ColD] = @ColD,

[ObjectID] = @objectID

WHERE [ObjectID] = @objectID;

PS You may want to update your original post and remove a USE statement that still contains what looks like real info.