A simple fix to this problem is to value the work that you guys each put in as salaries. You should have probably done this from the beginning but it is not too late.
You both own 50% of the company. That is fair, what is not fair is that you put in all the work while he lags.
What you could do is agree on a scale where each of you get paid for your efforts.
YOu could do this hourly or per task.
So you can tell your partner that work on the website is worth $20 per hour, while marketing work is worth $25 per hour, $15 for customer service and $22.50 for building relationships with vendors. Once you have all these values assigned (my examples will be different than your own business), then you divide up weekly tasks.
If this week you need to spend 10 hours on the site, 3 on marketing and 15 more on vendor relationships you bill your own company, as an employee accordingly:
So you bill:
10 x $20.0 = $200
03 x $25.0 = $75
15 x $22.5 = $337.50
Total = $612.50
The 612.50 becomes a business expense, and whatever is left over you guys still share 50/50. This way you are getting some value for the extra work you put in. Or if he decides to put in tons of work it is valued.
You want to make these rates equal to what someone else could do the work for.
Maybe a time will come when you only use employees or contracts to do the actual day to day work while you both share the 50/50 income.