Why energy of some intermediates of glycolysis increases?
Step 1:

Phosphorylation activates glucose for the following reactions in the pathway. However, the formation
of such a phosphoester is thermodynamically unfavourable and requires
energy input to operate in the forward direction. The energy comes
from ATP, a requirement that at first seems counterproductive.


  $$\ce{-D-Glucose + ATP^4- → -D-glucose-6-phosphate^2- + ADP3  H+}$$
  $\Delta G$ = -16.7 kJ/mol


and energy is released.

Step 3:

Once again, the substrate that provides the phosphoryl group is ATP. Like the hexokinase/
glucokinase reaction, the phosphorylation of fructose-6-phosphate is a priming
reaction and is endergonic(energy absorbed):


  Fructose-6-P + Pi +fructose-1,6-bisphosphate   $\Delta G$ = 16.3
  kJ/mol


When coupled (by phosphofructokinase) with the hydrolysis of ATP, the overall reaction
becomes exergonic:


  Fructose-6-P + ATP → fructose-1,6-bisphosphate + ADP 
  
  $\Delta G$ = -14.2 kJ/mol


Step 4:

Fructose bisphosphate aldolase cleaves fructose-1,6-bisphosphate between the
C-3 and C-4 carbons to yield two triose phosphates. The products are dihydroxyacetone
phosphate (DHAP) and glyceraldehyde-3-phosphate. The reaction has an
equilibrium constant of approximately 10^-4 M, and a corresponding $\Delta G$  of +23.9 kJ/mol.

(the equilibrium is thus greatly influenced by concentration.)

Step 6:

In the first glycolytic reaction to involve oxidation–reduction, glyceraldehyde-3-
phosphate is oxidized to 1,3-bisphosphoglycerate by glyceraldehyde-3-phosphate dehydrogenase.

Although the oxidation of an aldehyde to a carboxylic acid is a highly
exergonic reaction, the overall reaction involves both formation of a carboxylic–
phosphoric anhydride and the reduction of NAD to NADH and is therefore slightly
endergonic at standard state, with a $\Delta G$ of + 6.30 kJ/mol.

(The free energy that might otherwise be released as heat in this reaction is directed into the formation of
a high-energy phosphate compound, 1,3-bisphosphoglycerate, and the reduction of
NAD.)

Step 7:

Here the glycolytic pathway breaks even in terms of ATPs consumed and produced
with this reaction.The enzyme phosphoglycerate kinase transfers a phosphoryl
group from 1,3-bisphosphoglycerate to ADP to form an ATP.

The phosphoglycerate kinase reaction is sufficiently exergonic at
standard state to pull the G-3-P dehydrogenase reaction along. (In fact, the 
aldolase and triose phosphate isomerase are also pulled forward by phosphoglycerate
kinase.) The net result of these coupled reactions is


  Glyceraldehyde-3-phosphate + ADP + Pi + NAD → 3-phosphoglycerate + ATP
  + NADH + H+ $\Delta G$ = -12.6 kJ/mol 


(Important: Another reflection of the coupling between these reactions lies in their values
of $\Delta G$ under cellular conditions, despite its strongly negative  the phosphoglycerate kinase reaction operates at equilibrium in the erythrocyte ($\Delta G$ =0.1 kJ/mol).



So in this case you'ill notice factors that influence energy expenditure and gain. Step 1 and 3 (exegonic reactions have net -G hence ) will see energy being released (and accroding to your diagram 
there is a decrease. Conversely in Step in steps 4-5 (reaction not favoured but due to concentration proceeds and is aided by energy and 6-7( energy is absorbed to form a high energy compound
1,3-bisphosphoglycerate) and 7-8 is mainly determined by reaction environment and relative concentrations of substrates and is slightly endergonic in above case.

Hope this helps

Reference

Biochemistry 4th Ed (Grisham)