Update problem I cannot work out

I cannot work out how to do the following query

testdb=> select * from t1;
var1|var2
----+----
1| 2
2| 2
2| 3
(3 rows)

testdb=> select * from t2;
var1|var2
----+----
5| 2
9| 3
4| 4
(3 rows)

I need to add to the value of each var1 in t2 the sum of all var1's in t1
that have the same value corresponding var2's

testdb=> update t2 set var1=t2.var1+sum(t1.var1) where t1.var2=t2.var2;
ERROR: parser: illegal use of aggregates or non-group column in target list

I imagine that this is failing because it isnt sure which values to
sum(), but I cannot for the life of me figure out how to solve this.

My second idea was to do

testdb=> update t2 set var1=t2.var1+t1.var1 where t2.var2=t1.var1;
NOTICE: Non-functional update, only first update is performed
UPDATE 1

This will only, obviously, add one of the values I need to add.

The values I need to end up with, just so you know you are solving the
right problem, are:

testdb=> select * from t1;
var1|var2
----+----
1| 2
2| 2
2| 3
(3 rows)

testdb=> select * from t2;
var1|var2
----+----
8| 2
11| 3
4| 4
(3 rows)

Any help on this would be appreciated. I am a bit stuck here, and I am
sure I am just missing something blindingly obvious.
I am loathe to use a cursor to do this, because my actual dataset is
upwards of 10,000 records, and I do not wish to do 10,000 different
queries.