Is B-Tree re-balanced during deletion of data from SQL Server table with a clustered index? I have a table in a SQL Server database with a clustered index on the primary key. The table has 1 million rows. If I delete 10K rows from table, do index get restructured during deletion operation is performed ? 

The deletion operation is part of stored procedure. At a time, more than one client can be executing the stored procedure, however each individual run will delete it's own set of rows (uniquely identified by primary key). I'm getting blocking on Key lock (of type U) when multiple clients executes the procedure. The blocker lock belongs to a row from the same table and it is not part of any of the concurrently running transaction. There should not be any blocking as each run is trying to delete it's own set of rows. Lock escalation is not happening as it is turned off. 

I suspect, deletion operation must be causing index to re-balance and hence during restructuring process it can take key lock on any row of the table.

I would really appreciate any opinion on this.
To answer the question in the title, whether the B-tree rebalanced during a delete, the answer appears to be no, at least in the following minimal test case.

The following demo runs commands that are best left for a test environment.

--create table and fill it
DROP TABLE IF EXISTS bunchesofints
CREATE TABLE bunchesofints (
thisisanint INT PRIMARY KEY CLUSTERED,
junkrow CHAR(1000) NOT NULL
)

INSERT dbo.bunchesofints
SELECT TOP 5000
ROW_NUMBER() OVER(ORDER BY(SELECT NULL)) AS thisisanint,
REPLICATE('a',1000) AS junkrow
FROM sys.all_objects a1
CROSS JOIN sys.all_objects a2


--with this query we can see all the non-leaf pages of the b-tree, plus the IAM
SELECT allocated_page_page_id, page_type_desc, page_level, is_allocated, next_page_page_id, previous_page_page_id
FROM sys.dm_db_database_page_allocations(DB_ID(),OBJECT_ID('dbo.bunchesofints'),NULL,NULL,'DETAILED')
WHERE page_type != 1
GO

--Ok, let's delete most of the rows
;WITH CTE AS (
    SELECT TOP (4500) *
    FROM dbo.bunchesofints
    ORDER BY thisisanint DESC
)

DELETE 
FROM CTE
GO

--Hmm, still have 3 non-leaf index pages
SELECT allocated_page_page_id, page_type_desc, page_level, is_allocated, next_page_page_id, previous_page_page_id
FROM sys.dm_db_database_page_allocations(DB_ID(),OBJECT_ID('dbo.bunchesofints'),NULL,NULL,'DETAILED')
WHERE page_type != 1



--So, where are the rows?
--please note the assumption that your test database has a single file.
DECLARE @firstindexpage INT, @lastindexpage INT, @db INT = DB_ID()
SELECT @firstindexpage = MIN(previous_page_page_id), @lastindexpage = MAX(next_page_page_id)
FROM sys.dm_db_database_page_allocations(DB_ID(),OBJECT_ID('dbo.bunchesofints'),NULL,NULL,'DETAILED')
WHERE page_type = 2 AND page_level = 1

DBCC PAGE(@db,1,@firstindexpage,3) WITH TABLERESULTS
DBCC PAGE(@db,1,@lastindexpage,3) WITH TABLERESULTS


This demo shows that a delete can produce a very unbalanced b-tree, with practically all data on one side.