Please try the following solution based on SQL Server’s powerful XML and XQuery functionality.

It is generic regardless how many column pairs are across in the table. No need in any dynamic SQL.

The entire magic is based on the mod operator.

Notable points:

• 1st CROSS APPLY is converting all columns into XML data type.
• 2nd CROSS APPLY is re-shaping XML into a proper format based on XML attributes.
• 3rd CROSS APPLY is shredding XML back into relational/rectangular data.
• Post CTE SELECT is grouping and summing data.

To feel and see it, here is the first row x value has the following XML:

<root>
  <UserID1>1</UserID1>
  <Amount1>10</Amount1>
  <UserID2>2</UserID2>
  <Amount2>15</Amount2>
  <UserID3>125</UserID3>
  <Amount3>30</Amount3>
</root>

and the y has the following value:

<root>
  <r id="1" amount="10" />
  <r id="2" amount="15" />
  <r id="125" amount="30" />
</root>

The same for each row.

SQL

-- DDL and sample data population, start
DECLARE @tbl TABLE (UserID1 INT, Amount1 INT, UserID2 INT, Amount2 INT, UserID3 INT, Amount3 INT);
INSERT INTO @tbl (UserID1, Amount1, UserID2, Amount2, UserID3, Amount3) VALUES
(1  , 10, 2, 15, 125, 30),
(2  , 26, 5, 17, 3  , 26),
(125, 17, 3, 22, 1  , 20);
-- DDL and sample data population, end

WITH rs AS
(
    SELECT z.value('@id', 'INT') AS ID
        , z.value('@amount', 'INT') AS Amount
    FROM @tbl AS t
    CROSS APPLY (SELECT t.* FOR XML PATH(''), TYPE, ROOT('root')) AS t1(x)
    CROSS APPLY (SELECT x.query('<root>
       {
          for $x in /root/*[position() mod 2 = 1]
          let $pos := count(/root/*[. << $x[1]]) + 1
          return <r id="{$x/text()}" amount="{/root/*[$pos + 1]/text()}"></r>
       }
       </root>')) AS t2(y)
    CROSS APPLY y.nodes('/root/r') AS t3(z)
)
SELECT ID, SUM(Amount) AS Amount
FROM rs
GROUP BY ID
ORDER BY ID;

Output

If you are doing this as a one-off, you can use dynamic SQL:

declare @i integer=2, @sql as nvarchar(max)='select userId1 as UserId, Amount1 as Amount from YrTbl';
while @i <= 50 begin
  set @sql = @sql + ' union all' + char(10) + 
             N'select userId' 
                  + cast(@i  as nvarchar(10)) + N', '
                  + 'Amount'
                  + cast(@i  as nvarchar(10)) + N' from YrTbl'
  set @i=@i+1
end;
set @sql=N'select UserId, sum(Amount) as Amount  into #YrNewTable from (' + @sql + ') S1 group by UserId'
exec sp_executesql @sql
--print @sql

For production work careful consideration must be paid to security/performance aspects of dynamic SQL.

Alternative to looping:

declare @sql varchar(max);
set @sql=(SELECT string_agg('select ' + Column_name + ' as UserId, Amount' + substring(column_Name, 7,10) + ' as Amount from YrTbl union all', char(10))
            FROM tempdb.INFORMATION_SCHEMA.COLUMNS c 
            WHERE c.TABLE_NAME LIKE '#YrTbl%'
            and Column_Name like 'UserId%')
set @sql='select UserId, sum(Amount) as Amount) from (' 
         + lefT(@sql,len(@sql)-9)
         + ') S1 group by UserId'
exec sp_executesql@sql

One of the options to do it is using UNPIVOT to get your UserID-Amount pairs into rows and then to do aggregation:

WITH    --  S a m p l e    D a t a : 
  tbl (UserID1, Amount1, UserID2, Amount2, UserID3, Amount3) AS
    ( Select    1,  10,  2,  15,  125,  30 Union All
      Select    2,  26,  5,  17,    3,  26 Union All
      Select  125,  17,  3,  22,    1,  20
    ),

… create cte (pairs) to transpose columns to rows using UNPIVOT

  pairs as
    ( Select   Case  When UserID Is Null
                     Then LAG(UserID) Over(Partition By PAIR Order By PAIR)
               Else  UserID
               End as UserID, 
               Amount
      From    ( Select    COLUMN_PAIR, Right(COLUMN_PAIR, 1) as PAIR,
                          Case When Left(COLUMN_PAIR, 1) = 'U' Then Amount End as UserID, 
                          Case When Left(COLUMN_PAIR, 1) = 'A' Then Amount Else 0 End as Amount
                From      ( Select *
                            From   ( Select   *  From   tbl ) t
                            UNPIVOT ( Amount 
                                      FOR COLUMN_PAIR IN( UserID1, Amount1, 
                                                          UserID2, Amount2, 
                                                          UserID3, Amount3 )   
                                    ) u 
                         ) u
              ) u
    )

… aggregate (Sum) the amounts and group by UserID

--      M a i n    S Q L : 
Select    UserID, Sum(Amount) as Amount
From      pairs
Group By  UserID
Order By  UserID

/*
UserID  Amount
------  ------
     1      30
     2      41
     3      48
     5      17
   125      47      */

See the fiddle here.