Hi - retired TA here, over twenty years in primary schools.
Schools I've worked in were pretty flexible on moving children up a level or two, and as a TA I would tell the teacher if I thought a child needed to move (up, or down). Do you know if he is on a 'scheme' and are all the words 'decode-able' in books he is getting? That is excellent if he goes back and says the sentence with more expression. So many children, in the early stages, read like robots, and I would sometimes mimic that effect so they might realize it didn't sound too good. We used to tell children to "say it like talking".
A Reception class I spent some time in as a voluntary helper, children gave the 'impression' of reading, but in fact had done the book so many times they knew it off by heart, and would say text from pages when they weren't even looking at the correct page!
Do you test him to see if he really UNDERSTANDS what he is reading? When children are decoding and reading very slowly, the meaning can get lost. Ask him questions about the content, what might happen next, what other outcome might have been possible, what would HE have done in that situation, etc? (Many early books might be so simple that none of those questions would be relevant anyway).
Is there a TA or other helper in his class? Does he have a 'reading diary' where you can comment on his reading at home? Quite often in classes the teacher doesn't get to read individually with children very often, though they may well do group or shared reading.
Does he have a go at writing words himself? A small 'white board' or lots of paper at home is good so he can try 'emergent writing' for himself. Don't give too much help, but see what he can manage for himself. 'Having a go' is more important than the end result at this stage. Or writing with a finger on a thin layer of sand or flour on a large, shallow tray is good for letter formation.
If his teacher is friendly towards parents, there is no reason why you shouldn't enquire about how it all works! Some schools have parent 'workshops' to explain subject to parents.
And don't neglect Numeracy; count things with him, look at how numbers are used - in measuring, weighing, clocks etc.