Update statement with a function

The performance impact from multiple logical reads could be a result of your UDF.

Provided is a great article which describes using inline table-valued UDFs to reduce the row-by-row calls to the scalar UDF. UPDATE: I noticed you were already using table-valued UDF.

http://dataeducation.com/scalar-functions-inlining-and-performance-an-entertaining-title-for-a-boring-post/

To replicate your scenario, I executed the following query:

DECLARE
   @Measurements TABLE(Precidence int, -- the relative scale of a measurement
             Measurement varchar(max), -- Grams, Kilograms, Liters, etc
             MeasurementType varchar(max)); -- Weight, Volume, etc`

DECLARE
   @Items TABLE(ItemType varchar(max),   
            Quantity float,  
            Measurement varchar(max),   
            ToMeasurement varchar(max));

insert into @items (ItemType, Quantity, Measurement) values ('Widget','1','G');  
insert into @items (ItemType, Quantity, Measurement) values ('Widget','1','KG');  
insert into @items (ItemType, Quantity, Measurement) values ('Widget','1','ML');  
insert into @items (ItemType, Quantity, Measurement) values ('Widget','1','L'); 

insert into @Measurements (Precidence, Measurement, MeasurementType) values ('2','G','Weight');  
insert into @Measurements (Precidence, Measurement, MeasurementType) values ('1','KG','Weight');  
insert into @Measurements (Precidence, Measurement, MeasurementType) values ('1','GAL','Volume');  
insert into @Measurements (Precidence, Measurement, MeasurementType) values ('2','L','Volume');  
insert into @Measurements (Precidence, Measurement, MeasurementType) values ('3','ML','Volume'); 

Afterwards, I complied and executed the following update statement:

WITH Items_CTE AS
   (
        SELECT A.ItemType, 
               A.Quantity,
               A.Measurement,  
               (SELECT TOP 1 M.Measurement FROM @Measurements M
                JOIN @Items C ON C.Measurement = M.Measurement
                WHERE M.MeasurementType = B.MeasurementType
                AND  C.ItemType = A.ItemType
                 ORDER BY Precidence)ToMeasurement
       FROM @Items A
       JOIN @Measurements B
       ON A.Measurement = B.Measurement
    )  
UPDATE @Items  
SET ToMeasurement = cte.ToMeasurement  
FROM ITEMS_CTE as cte
JOIN @Items as i
ON cte.measurement = i.measurement;

The UPDATE statement uses a CTE and the results were as follows:

ItemType | Quantity | Measurement | ToMeasurement  
Widget   |    1     |    G        |    KG  
Widget   |    1     |    KG       |    KG  
Widget   |    1     |    ML       |    L  
Widget   |    1     |    L        |    L

To be less ambiguous you can prepend the alias in the set clause. (Taken from 孔夫子 in the comments, who did not submit an answer.)

update address
set a1.col1 = a2.col1,
a1.col2 = a2.col2,
.....etc
from address a1, address a2
where a1.id = @to and a2.id = @from