Heavy Legs

Out running this morning, got to about 30 minutes and my legs felt really heavy.  My breathing was fine, I generally felt ok but my legs just felt heavy.  I carried on running and they seemed to go back to normal

Is this normal, Is it just my body adjusting (I have only been running 3 x week for 2 weeks)?

Aye - perfectly normal.

Part of being human is that somedays it feels easier than others, some days you start  with heavy legs and they will get worse but more often than not they feel better after warming up.

If it persists for a few runs, then maybe take an extra day or so off.  Your legs are adjusting to the new demands that running puts upon it - they'll be able to cope but sometimes they just need a couple of extra days to adapt.

Thanks for the response, I have another question

At the weekend I found it really hard going.  Out of breath after 10 minutes and i never really recovered so ended it doing walk/run/walk/run.

Today, seemed much easier

I know some runs are tougher but the weekend run was really hard, as if I had never run before.  It was later in the day (1pm) than my normal runs (6am) and i had been out walking the dog beforehand.  i must also confess to having a couple of beers the night before.  I am putting it down to these things rather than anything major but again I wonder if bad runs are part of the deal?

Also, is it natural for the first part of the run to be faster

I ran my first 12 minutes at a pace of 5:37, my second was 6:20 and my third 06:13.

Should I be targetting a steady pace for the entire run?

Lots of questions!

Yes, you will experience the odd "bad" run.  The key for improvement is to identify the differences between good & bad runs.  For example, from what you've said the change in time wouldn't affect me, and I wouldn't expect to expend too much energy walking the dog - but I know I will be significantly slower for a given level of effort if I've had a drink the night before. However everyone's different, and the change in time/dog walk may have had an influence on you (although the most likely culprit is the beer!).  Personally I just accept that if I'm going to be drinking, then the next day's run won't be as easy. 

For the average runner an even pace is the best target (for top-level runners, a negative split is often quoted as the ideal) .  You are making the common beginner's mistake of running too fast at the start.  Just slow down and take it easy , try running at a pace that you could maintain conversation if you were running with someone.  It does sound counter-intuitive, but by running at a pace that feels comfortably hard you are getting the least benefit from your running.  By running slower you will give your body a chance to adapt & build your leg muscles for your running, whereas by running too fast your body is too busy repairing the damage to have anything leftover to build upon your existing muscle.   

Thanks some really helpful advice in the replies